%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN080+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 : Thu Jul 21 08:59:24 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 16 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 12 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 30 ( 8 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel58_1,axiom,
! [X,Y] : f(X) = g(Y) ).
fof(pel58,conjecture,
! [X,Y] : f(f(X)) = f(g(Y)) ).
fof(subgoal_0,plain,
! [X,Y] : f(f(X)) = f(g(Y)),
inference(strip,[],[pel58]) ).
fof(negate_0_0,plain,
~ ! [X,Y] : f(f(X)) = f(g(Y)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X,Y] : f(f(X)) != f(g(Y)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
f(f(skolemFOFtoCNF_X)) != f(g(skolemFOFtoCNF_Y)),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] : f(X) = g(Y),
inference(canonicalize,[],[pel58_1]) ).
fof(normalize_0_3,plain,
! [X,Y] : f(X) = g(Y),
inference(specialize,[],[normalize_0_2]) ).
cnf(refute_0_0,plain,
f(f(skolemFOFtoCNF_X)) != f(g(skolemFOFtoCNF_Y)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
f(X) = g(Y),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
f(f(skolemFOFtoCNF_X)) = g(X_1),
inference(subst,[],[refute_0_1:[bind(X,$fot(f(skolemFOFtoCNF_X))),bind(Y,$fot(X_1))]]) ).
cnf(refute_0_3,plain,
( f(f(skolemFOFtoCNF_X)) != g(X_1)
| g(X_1) != f(g(skolemFOFtoCNF_Y))
| f(f(skolemFOFtoCNF_X)) = f(g(skolemFOFtoCNF_Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(f(skolemFOFtoCNF_X)),f(g(skolemFOFtoCNF_Y))) ),[0],$fot(g(X_1))]]) ).
cnf(refute_0_4,plain,
( g(X_1) != f(g(skolemFOFtoCNF_Y))
| f(f(skolemFOFtoCNF_X)) = f(g(skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( $equal(f(f(skolemFOFtoCNF_X)),g(X_1)) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
g(X_1) != f(g(skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( $equal(f(f(skolemFOFtoCNF_X)),f(g(skolemFOFtoCNF_Y))) )],[refute_0_4,refute_0_0]) ).
cnf(refute_0_6,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_7,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_8,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( f(X) != g(Y)
| g(Y) = f(X) ),
inference(subst,[],[refute_0_8:[bind(X0,$fot(f(X))),bind(Y0,$fot(g(Y)))]]) ).
cnf(refute_0_10,plain,
g(Y) = f(X),
inference(resolve,[$cnf( $equal(f(X),g(Y)) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
g(X_1) = f(g(skolemFOFtoCNF_Y)),
inference(subst,[],[refute_0_10:[bind(X,$fot(g(skolemFOFtoCNF_Y))),bind(Y,$fot(X_1))]]) ).
cnf(refute_0_12,plain,
$false,
inference(resolve,[$cnf( $equal(g(X_1),f(g(skolemFOFtoCNF_Y))) )],[refute_0_11,refute_0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN080+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 11 18:46:47 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35
%------------------------------------------------------------------------------