%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN351+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 09:01:40 EDT 2022
% Result : Theorem 0.13s 0.34s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 88 ( 0 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 99 ( 30 ~; 11 |; 28 &)
% ( 15 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 2 sgn 27 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_18_3,conjecture,
! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,Y2,X1,Z)
=> ( ( big_f(X1,Y1,X1,Y2)
<=> big_f(Y1,X2,Y1,Y2) )
=> ( big_f(X1,Y1,X1,Y2)
=> ( ( big_f(X1,Y2,Y1,Y2)
=> big_f(X1,Z,Y1,Z) )
& ( big_f(X1,Z,Y1,Z)
=> ( big_f(X1,Y1,X1,Y2)
<=> big_f(X1,Y2,Y1,Y2) ) ) ) ) ) ) ).
fof(subgoal_0,plain,
! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,Y2,X1,Z)
=> ( ( big_f(X1,Y1,X1,Y2)
<=> big_f(Y1,X2,Y1,Y2) )
=> ( big_f(X1,Y1,X1,Y2)
=> ( ( big_f(X1,Y2,Y1,Y2)
=> big_f(X1,Z,Y1,Z) )
& ( big_f(X1,Z,Y1,Z)
=> ( big_f(X1,Y1,X1,Y2)
<=> big_f(X1,Y2,Y1,Y2) ) ) ) ) ) ),
inference(strip,[],[church_46_18_3]) ).
fof(negate_0_0,plain,
~ ! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,Y2,X1,Z)
=> ( ( big_f(X1,Y1,X1,Y2)
<=> big_f(Y1,X2,Y1,Y2) )
=> ( big_f(X1,Y1,X1,Y2)
=> ( ( big_f(X1,Y2,Y1,Y2)
=> big_f(X1,Z,Y1,Z) )
& ( big_f(X1,Z,Y1,Z)
=> ( big_f(X1,Y1,X1,Y2)
<=> big_f(X1,Y2,Y1,Y2) ) ) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X1,X2] :
! [Y1,Y2] :
? [Z] :
( big_f(X1,Y1,X1,Y2)
& big_f(X1,Y2,X1,Z)
& ( ( ~ big_f(X1,Z,Y1,Z)
& big_f(X1,Y2,Y1,Y2) )
| ( big_f(X1,Z,Y1,Z)
& ( ~ big_f(X1,Y1,X1,Y2)
<=> big_f(X1,Y2,Y1,Y2) ) ) )
& ( ~ big_f(X1,Y1,X1,Y2)
<=> ~ big_f(Y1,X2,Y1,Y2) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [Y1,Y2] :
? [Z] :
( big_f(skolemFOFtoCNF_X1,Y1,skolemFOFtoCNF_X1,Y2)
& big_f(skolemFOFtoCNF_X1,Y2,skolemFOFtoCNF_X1,Z)
& ( ( ~ big_f(skolemFOFtoCNF_X1,Z,Y1,Z)
& big_f(skolemFOFtoCNF_X1,Y2,Y1,Y2) )
| ( big_f(skolemFOFtoCNF_X1,Z,Y1,Z)
& ( ~ big_f(skolemFOFtoCNF_X1,Y1,skolemFOFtoCNF_X1,Y2)
<=> big_f(skolemFOFtoCNF_X1,Y2,Y1,Y2) ) ) )
& ( ~ big_f(Y1,skolemFOFtoCNF_X2,Y1,Y2)
<=> ~ big_f(skolemFOFtoCNF_X1,Y1,skolemFOFtoCNF_X1,Y2) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [Y1,Y2] :
? [Z] :
( big_f(skolemFOFtoCNF_X1,Y1,skolemFOFtoCNF_X1,Y2)
& big_f(skolemFOFtoCNF_X1,Y2,skolemFOFtoCNF_X1,Z)
& ( ( ~ big_f(skolemFOFtoCNF_X1,Z,Y1,Z)
& big_f(skolemFOFtoCNF_X1,Y2,Y1,Y2) )
| ( big_f(skolemFOFtoCNF_X1,Z,Y1,Z)
& ( ~ big_f(skolemFOFtoCNF_X1,Y1,skolemFOFtoCNF_X1,Y2)
<=> big_f(skolemFOFtoCNF_X1,Y2,Y1,Y2) ) ) )
& ( ~ big_f(Y1,skolemFOFtoCNF_X2,Y1,Y2)
<=> ~ big_f(skolemFOFtoCNF_X1,Y1,skolemFOFtoCNF_X1,Y2) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [Y1,Y2] :
( big_f(skolemFOFtoCNF_X1,Y1,skolemFOFtoCNF_X1,Y2)
& big_f(skolemFOFtoCNF_X1,Y2,skolemFOFtoCNF_X1,skolemFOFtoCNF_Z(Y1,Y2))
& ( ( ~ big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_Z(Y1,Y2),Y1,skolemFOFtoCNF_Z(Y1,Y2))
& big_f(skolemFOFtoCNF_X1,Y2,Y1,Y2) )
| ( big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_Z(Y1,Y2),Y1,skolemFOFtoCNF_Z(Y1,Y2))
& ( ~ big_f(skolemFOFtoCNF_X1,Y1,skolemFOFtoCNF_X1,Y2)
<=> big_f(skolemFOFtoCNF_X1,Y2,Y1,Y2) ) ) )
& ( ~ big_f(Y1,skolemFOFtoCNF_X2,Y1,Y2)
<=> ~ big_f(skolemFOFtoCNF_X1,Y1,skolemFOFtoCNF_X1,Y2) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [Y1,Y2] : big_f(skolemFOFtoCNF_X1,Y1,skolemFOFtoCNF_X1,Y2),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [Y1,Y2] :
( ( ~ big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_Z(Y1,Y2),Y1,skolemFOFtoCNF_Z(Y1,Y2))
& big_f(skolemFOFtoCNF_X1,Y2,Y1,Y2) )
| ( big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_Z(Y1,Y2),Y1,skolemFOFtoCNF_Z(Y1,Y2))
& ( ~ big_f(skolemFOFtoCNF_X1,Y1,skolemFOFtoCNF_X1,Y2)
<=> big_f(skolemFOFtoCNF_X1,Y2,Y1,Y2) ) ) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_6,plain,
! [Y1,Y2] :
( ( ~ big_f(skolemFOFtoCNF_X1,Y2,Y1,Y2)
& big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_Z(Y1,Y2),Y1,skolemFOFtoCNF_Z(Y1,Y2)) )
| ( ~ big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_Z(Y1,Y2),Y1,skolemFOFtoCNF_Z(Y1,Y2))
& big_f(skolemFOFtoCNF_X1,Y2,Y1,Y2) ) ),
inference(simplify,[],[normalize_0_5,normalize_0_4]) ).
fof(normalize_0_7,plain,
! [Y1,Y2] :
( ( ~ big_f(skolemFOFtoCNF_X1,Y2,Y1,Y2)
| ~ big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_Z(Y1,Y2),Y1,skolemFOFtoCNF_Z(Y1,Y2)) )
& ( big_f(skolemFOFtoCNF_X1,Y2,Y1,Y2)
| big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_Z(Y1,Y2),Y1,skolemFOFtoCNF_Z(Y1,Y2)) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [Y1,Y2] :
( ~ big_f(skolemFOFtoCNF_X1,Y2,Y1,Y2)
| ~ big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_Z(Y1,Y2),Y1,skolemFOFtoCNF_Z(Y1,Y2)) ),
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
big_f(skolemFOFtoCNF_X1,Y1,skolemFOFtoCNF_X1,Y2),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_Z(skolemFOFtoCNF_X1,X_7),skolemFOFtoCNF_X1,skolemFOFtoCNF_Z(skolemFOFtoCNF_X1,X_7)),
inference(subst,[],[refute_0_0:[bind(Y1,$fot(skolemFOFtoCNF_Z(skolemFOFtoCNF_X1,X_7))),bind(Y2,$fot(skolemFOFtoCNF_Z(skolemFOFtoCNF_X1,X_7)))]]) ).
cnf(refute_0_2,plain,
( ~ big_f(skolemFOFtoCNF_X1,Y2,Y1,Y2)
| ~ big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_Z(Y1,Y2),Y1,skolemFOFtoCNF_Z(Y1,Y2)) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_3,plain,
( ~ big_f(skolemFOFtoCNF_X1,X_7,skolemFOFtoCNF_X1,X_7)
| ~ big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_Z(skolemFOFtoCNF_X1,X_7),skolemFOFtoCNF_X1,skolemFOFtoCNF_Z(skolemFOFtoCNF_X1,X_7)) ),
inference(subst,[],[refute_0_2:[bind(Y1,$fot(skolemFOFtoCNF_X1)),bind(Y2,$fot(X_7))]]) ).
cnf(refute_0_4,plain,
~ big_f(skolemFOFtoCNF_X1,X_7,skolemFOFtoCNF_X1,X_7),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_Z(skolemFOFtoCNF_X1,X_7),skolemFOFtoCNF_X1,skolemFOFtoCNF_Z(skolemFOFtoCNF_X1,X_7)) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
big_f(skolemFOFtoCNF_X1,X_7,skolemFOFtoCNF_X1,X_7),
inference(subst,[],[refute_0_0:[bind(Y1,$fot(X_7)),bind(Y2,$fot(X_7))]]) ).
cnf(refute_0_6,plain,
$false,
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X1,X_7,skolemFOFtoCNF_X1,X_7) )],[refute_0_5,refute_0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN351+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jul 12 06:29:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34
% 0.13/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35
%------------------------------------------------------------------------------