TSTP Solution File: SYN350+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN350+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 09:01:39 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 114 ( 48 ~; 28 |; 16 &)
% ( 16 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 57 ( 6 sgn 30 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_18_2,conjecture,
! [X] :
? [Y1,Y2] :
! [Z] :
( ( big_f(X,Z)
<=> big_f(Z,X) )
=> ( big_f(X,Z)
<=> ( big_f(Y2,Z)
& ( big_f(Y1,Z)
=> big_f(Y1,Y2) ) ) ) ) ).
fof(subgoal_0,plain,
! [X] :
? [Y1,Y2] :
! [Z] :
( ( big_f(X,Z)
<=> big_f(Z,X) )
=> ( big_f(X,Z)
<=> ( big_f(Y2,Z)
& ( big_f(Y1,Z)
=> big_f(Y1,Y2) ) ) ) ),
inference(strip,[],[church_46_18_2]) ).
fof(negate_0_0,plain,
~ ! [X] :
? [Y1,Y2] :
! [Z] :
( ( big_f(X,Z)
<=> big_f(Z,X) )
=> ( big_f(X,Z)
<=> ( big_f(Y2,Z)
& ( big_f(Y1,Z)
=> big_f(Y1,Y2) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X] :
! [Y1,Y2] :
? [Z] :
( ( ~ big_f(X,Z)
<=> ~ big_f(Z,X) )
& ( ~ big_f(X,Z)
<=> ( big_f(Y2,Z)
& ( ~ big_f(Y1,Z)
| big_f(Y1,Y2) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [Y1,Y2] :
? [Z] :
( ( ~ big_f(Z,skolemFOFtoCNF_X)
<=> ~ big_f(skolemFOFtoCNF_X,Z) )
& ( ~ big_f(skolemFOFtoCNF_X,Z)
<=> ( big_f(Y2,Z)
& ( ~ big_f(Y1,Z)
| big_f(Y1,Y2) ) ) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [Y1,Y2] :
? [Z] :
( ( ~ big_f(Z,skolemFOFtoCNF_X)
<=> ~ big_f(skolemFOFtoCNF_X,Z) )
& ( ~ big_f(skolemFOFtoCNF_X,Z)
<=> ( big_f(Y2,Z)
& ( ~ big_f(Y1,Z)
| big_f(Y1,Y2) ) ) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [Y1,Y2] :
( ( ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2))
<=> ~ big_f(skolemFOFtoCNF_Z(Y1,Y2),skolemFOFtoCNF_X) )
& ( ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2))
<=> ( big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
& ( ~ big_f(Y1,skolemFOFtoCNF_Z(Y1,Y2))
| big_f(Y1,Y2) ) ) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [Y1,Y2] :
( ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2))
<=> ( big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
& ( ~ big_f(Y1,skolemFOFtoCNF_Z(Y1,Y2))
| big_f(Y1,Y2) ) ) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [Y1,Y2] :
( ( big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
| big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2)) )
& ( ~ big_f(Y1,Y2)
| ~ big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
| ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2)) )
& ( ~ big_f(Y1,skolemFOFtoCNF_Z(Y1,Y2))
| big_f(Y1,Y2)
| big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2)) )
& ( ~ big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
| ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2))
| big_f(Y1,skolemFOFtoCNF_Z(Y1,Y2)) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [Y1,Y2] :
( ~ big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
| ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2))
| big_f(Y1,skolemFOFtoCNF_Z(Y1,Y2)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [Y1,Y2] :
( big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
| big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2)) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_8,plain,
! [Y1,Y2] :
( ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2))
<=> ~ big_f(skolemFOFtoCNF_Z(Y1,Y2),skolemFOFtoCNF_X) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_9,plain,
! [Y1,Y2] :
( ( ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2))
| big_f(skolemFOFtoCNF_Z(Y1,Y2),skolemFOFtoCNF_X) )
& ( ~ big_f(skolemFOFtoCNF_Z(Y1,Y2),skolemFOFtoCNF_X)
| big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2)) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [Y1,Y2] :
( ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2))
| big_f(skolemFOFtoCNF_Z(Y1,Y2),skolemFOFtoCNF_X) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [Y1,Y2] :
( ~ big_f(Y1,Y2)
| ~ big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
| ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2)) ),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( ~ big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
| ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2))
| big_f(Y1,skolemFOFtoCNF_Z(Y1,Y2)) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_1,plain,
( ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,skolemFOFtoCNF_X))
| big_f(Y1,skolemFOFtoCNF_Z(Y1,skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_0:[bind(Y2,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_2,plain,
( big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
| big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,skolemFOFtoCNF_X)),
inference(subst,[],[refute_0_2:[bind(Y2,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_4,plain,
big_f(Y1,skolemFOFtoCNF_Z(Y1,skolemFOFtoCNF_X)),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,skolemFOFtoCNF_X)) )],[refute_0_3,refute_0_1]) ).
cnf(refute_0_5,plain,
big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(skolemFOFtoCNF_X,skolemFOFtoCNF_X)),
inference(subst,[],[refute_0_4:[bind(Y1,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_6,plain,
( ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2))
| big_f(skolemFOFtoCNF_Z(Y1,Y2),skolemFOFtoCNF_X) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_7,plain,
( ~ big_f(Y1,Y2)
| ~ big_f(Y2,skolemFOFtoCNF_Z(Y1,Y2))
| ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_8,plain,
( ~ big_f(Y1,skolemFOFtoCNF_X)
| ~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_7:[bind(Y2,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_9,plain,
~ big_f(Y1,skolemFOFtoCNF_X),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,skolemFOFtoCNF_X)) )],[refute_0_3,refute_0_8]) ).
cnf(refute_0_10,plain,
~ big_f(skolemFOFtoCNF_Z(Y1,Y2),skolemFOFtoCNF_X),
inference(subst,[],[refute_0_9:[bind(Y1,$fot(skolemFOFtoCNF_Z(Y1,Y2)))]]) ).
cnf(refute_0_11,plain,
~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(Y1,Y2)),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z(Y1,Y2),skolemFOFtoCNF_X) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
~ big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(skolemFOFtoCNF_X,skolemFOFtoCNF_X)),
inference(subst,[],[refute_0_11:[bind(Y1,$fot(skolemFOFtoCNF_X)),bind(Y2,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_13,plain,
$false,
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X,skolemFOFtoCNF_Z(skolemFOFtoCNF_X,skolemFOFtoCNF_X)) )],[refute_0_5,refute_0_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN350+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 11:26:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35
%------------------------------------------------------------------------------