TSTP Solution File: SYN083+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN083+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 08:59:26 EDT 2022
% Result : Theorem 0.14s 0.36s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 18 unt; 0 def)
% Number of atoms : 41 ( 40 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 19 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 21 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p61_1,axiom,
! [X,Y,Z] : f(X,f(Y,Z)) = f(f(X,Y),Z) ).
fof(pel61,conjecture,
! [X,Y,Z,W] : f(X,f(Y,f(Z,W))) = f(f(f(X,Y),Z),W) ).
fof(subgoal_0,plain,
! [X,Y,Z,W] : f(X,f(Y,f(Z,W))) = f(f(f(X,Y),Z),W),
inference(strip,[],[pel61]) ).
fof(negate_0_0,plain,
~ ! [X,Y,Z,W] : f(X,f(Y,f(Z,W))) = f(f(f(X,Y),Z),W),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [W,X,Y,Z] : f(X,f(Y,f(Z,W))) != f(f(f(X,Y),Z),W),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W))) != f(f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z),skolemFOFtoCNF_W),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y,Z] : f(X,f(Y,Z)) = f(f(X,Y),Z),
inference(canonicalize,[],[p61_1]) ).
fof(normalize_0_3,plain,
! [X,Y,Z] : f(X,f(Y,Z)) = f(f(X,Y),Z),
inference(specialize,[],[normalize_0_2]) ).
cnf(refute_0_0,plain,
f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W))) != f(f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z),skolemFOFtoCNF_W),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
f(X,f(Y,Z)) = f(f(X,Y),Z),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_3,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_4,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( f(X,f(Y,Z)) != f(f(X,Y),Z)
| f(f(X,Y),Z) = f(X,f(Y,Z)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(f(X,f(Y,Z)))),bind(Y0,$fot(f(f(X,Y),Z)))]]) ).
cnf(refute_0_6,plain,
f(f(X,Y),Z) = f(X,f(Y,Z)),
inference(resolve,[$cnf( $equal(f(X,f(Y,Z)),f(f(X,Y),Z)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W)) = f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W))),
inference(subst,[],[refute_0_6:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W)))]]) ).
cnf(refute_0_8,plain,
f(f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z),skolemFOFtoCNF_W) = f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W)),
inference(subst,[],[refute_0_6:[bind(X,$fot(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(skolemFOFtoCNF_Z)),bind(Z,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_9,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_10,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_4,refute_0_9]) ).
cnf(refute_0_11,plain,
( f(f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z),skolemFOFtoCNF_W) != f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W))
| f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W)) != f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W)))
| f(f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z),skolemFOFtoCNF_W) = f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W))) ),
inference(subst,[],[refute_0_10:[bind(X0,$fot(f(f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z),skolemFOFtoCNF_W))),bind(Y0,$fot(f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W)))),bind(Z0,$fot(f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W)))))]]) ).
cnf(refute_0_12,plain,
( f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W)) != f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W)))
| f(f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z),skolemFOFtoCNF_W) = f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W))) ),
inference(resolve,[$cnf( $equal(f(f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z),skolemFOFtoCNF_W),f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W))) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
f(f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z),skolemFOFtoCNF_W) = f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W))),
inference(resolve,[$cnf( $equal(f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W)),f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W)))) )],[refute_0_7,refute_0_12]) ).
cnf(refute_0_14,plain,
( f(f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z),skolemFOFtoCNF_W) != f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W)))
| f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W))) != f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W)))
| f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W))) = f(f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z),skolemFOFtoCNF_W) ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W))),f(f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z),skolemFOFtoCNF_W)) ),[1],$fot(f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W))))]]) ).
cnf(refute_0_15,plain,
( f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W))) != f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W)))
| f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W))) = f(f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z),skolemFOFtoCNF_W) ),
inference(resolve,[$cnf( $equal(f(f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z),skolemFOFtoCNF_W),f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W)))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W))) != f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W))),
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W))),f(f(f(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z),skolemFOFtoCNF_W)) )],[refute_0_15,refute_0_0]) ).
cnf(refute_0_17,plain,
f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W))) = f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W))),
introduced(tautology,[refl,[$fot(f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W))))]]) ).
cnf(refute_0_18,plain,
$false,
inference(resolve,[$cnf( $equal(f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W))),f(skolemFOFtoCNF_X,f(skolemFOFtoCNF_Y,f(skolemFOFtoCNF_Z,skolemFOFtoCNF_W)))) )],[refute_0_17,refute_0_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN083+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n026.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 : Tue Jul 12 09:01:57 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36
% 0.14/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.37
%------------------------------------------------------------------------------