TSTP Solution File: SYN354+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN354+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 09:01:42 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 27 ( 6 unt; 0 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 164 ( 60 ~; 48 |; 23 &)
% ( 15 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 1 sgn 27 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_20_1,conjecture,
! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,X2)
=> ( big_g(X1,X2)
=> ( ( ( big_g(X2,Z)
<=> big_g(Y2,Z) )
=> ( big_f(Y1,Y2)
=> big_f(X2,Y2) ) )
=> ( ( big_g(X2,Z)
<=> big_g(Y1,Z) )
=> ( big_f(X1,Y1)
& big_f(X2,Y1)
& big_f(Y1,Y2) ) ) ) ) ) ).
fof(subgoal_0,plain,
! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,X2)
=> ( big_g(X1,X2)
=> ( ( ( big_g(X2,Z)
<=> big_g(Y2,Z) )
=> ( big_f(Y1,Y2)
=> big_f(X2,Y2) ) )
=> ( ( big_g(X2,Z)
<=> big_g(Y1,Z) )
=> ( big_f(X1,Y1)
& big_f(X2,Y1)
& big_f(Y1,Y2) ) ) ) ) ),
inference(strip,[],[church_46_20_1]) ).
fof(negate_0_0,plain,
~ ! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,X2)
=> ( big_g(X1,X2)
=> ( ( ( big_g(X2,Z)
<=> big_g(Y2,Z) )
=> ( big_f(Y1,Y2)
=> big_f(X2,Y2) ) )
=> ( ( big_g(X2,Z)
<=> big_g(Y1,Z) )
=> ( big_f(X1,Y1)
& big_f(X2,Y1)
& big_f(Y1,Y2) ) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X1,X2] :
! [Y1,Y2] :
? [Z] :
( big_f(X1,X2)
& big_g(X1,X2)
& ( ~ big_f(X1,Y1)
| ~ big_f(X2,Y1)
| ~ big_f(Y1,Y2) )
& ( ~ big_f(Y1,Y2)
| big_f(X2,Y2)
| ( ~ big_g(X2,Z)
<=> big_g(Y2,Z) ) )
& ( ~ big_g(X2,Z)
<=> ~ big_g(Y1,Z) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [Y1,Y2] :
? [Z] :
( big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)
& big_g(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)
& ( ~ big_f(Y1,Y2)
| ~ big_f(skolemFOFtoCNF_X1,Y1)
| ~ big_f(skolemFOFtoCNF_X2,Y1) )
& ( ~ big_f(Y1,Y2)
| big_f(skolemFOFtoCNF_X2,Y2)
| ( ~ big_g(Y2,Z)
<=> big_g(skolemFOFtoCNF_X2,Z) ) )
& ( ~ big_g(Y1,Z)
<=> ~ big_g(skolemFOFtoCNF_X2,Z) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [Y1,Y2] :
? [Z] :
( big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)
& big_g(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)
& ( ~ big_f(Y1,Y2)
| ~ big_f(skolemFOFtoCNF_X1,Y1)
| ~ big_f(skolemFOFtoCNF_X2,Y1) )
& ( ~ big_f(Y1,Y2)
| big_f(skolemFOFtoCNF_X2,Y2)
| ( ~ big_g(Y2,Z)
<=> big_g(skolemFOFtoCNF_X2,Z) ) )
& ( ~ big_g(Y1,Z)
<=> ~ big_g(skolemFOFtoCNF_X2,Z) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [Y1,Y2] :
( big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)
& big_g(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)
& ( ~ big_f(Y1,Y2)
| ~ big_f(skolemFOFtoCNF_X1,Y1)
| ~ big_f(skolemFOFtoCNF_X2,Y1) )
& ( ~ big_f(Y1,Y2)
| big_f(skolemFOFtoCNF_X2,Y2)
| ( ~ big_g(Y2,skolemFOFtoCNF_Z(Y1,Y2))
<=> big_g(skolemFOFtoCNF_X2,skolemFOFtoCNF_Z(Y1,Y2)) ) )
& ( ~ big_g(Y1,skolemFOFtoCNF_Z(Y1,Y2))
<=> ~ big_g(skolemFOFtoCNF_X2,skolemFOFtoCNF_Z(Y1,Y2)) ) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [Y1,Y2] :
( ~ big_f(Y1,Y2)
| big_f(skolemFOFtoCNF_X2,Y2)
| ( ~ big_g(Y2,skolemFOFtoCNF_Z(Y1,Y2))
<=> big_g(skolemFOFtoCNF_X2,skolemFOFtoCNF_Z(Y1,Y2)) ) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [Y1,Y2] :
( ( ~ big_f(Y1,Y2)
| ~ big_g(Y2,skolemFOFtoCNF_Z(Y1,Y2))
| ~ big_g(skolemFOFtoCNF_X2,skolemFOFtoCNF_Z(Y1,Y2))
| big_f(skolemFOFtoCNF_X2,Y2) )
& ( ~ big_f(Y1,Y2)
| big_f(skolemFOFtoCNF_X2,Y2)
| big_g(Y2,skolemFOFtoCNF_Z(Y1,Y2))
| big_g(skolemFOFtoCNF_X2,skolemFOFtoCNF_Z(Y1,Y2)) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [Y1,Y2] :
( ~ big_f(Y1,Y2)
| ~ big_g(Y2,skolemFOFtoCNF_Z(Y1,Y2))
| ~ big_g(skolemFOFtoCNF_X2,skolemFOFtoCNF_Z(Y1,Y2))
| big_f(skolemFOFtoCNF_X2,Y2) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [Y1,Y2] :
( ~ big_f(Y1,Y2)
| ~ big_f(skolemFOFtoCNF_X1,Y1)
| ~ big_f(skolemFOFtoCNF_X2,Y1) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_8,plain,
big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_9,plain,
! [Y1,Y2] :
( ~ big_f(Y1,Y2)
| big_f(skolemFOFtoCNF_X2,Y2)
| big_g(Y2,skolemFOFtoCNF_Z(Y1,Y2))
| big_g(skolemFOFtoCNF_X2,skolemFOFtoCNF_Z(Y1,Y2)) ),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( ~ big_f(Y1,Y2)
| ~ big_g(Y2,skolemFOFtoCNF_Z(Y1,Y2))
| ~ big_g(skolemFOFtoCNF_X2,skolemFOFtoCNF_Z(Y1,Y2))
| big_f(skolemFOFtoCNF_X2,Y2) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_1,plain,
( ~ big_f(Y1,skolemFOFtoCNF_X2)
| ~ big_g(skolemFOFtoCNF_X2,skolemFOFtoCNF_Z(Y1,skolemFOFtoCNF_X2))
| big_f(skolemFOFtoCNF_X2,skolemFOFtoCNF_X2) ),
inference(subst,[],[refute_0_0:[bind(Y2,$fot(skolemFOFtoCNF_X2))]]) ).
cnf(refute_0_2,plain,
( ~ big_f(Y1,Y2)
| ~ big_f(skolemFOFtoCNF_X1,Y1)
| ~ big_f(skolemFOFtoCNF_X2,Y1) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)
| ~ big_f(skolemFOFtoCNF_X2,skolemFOFtoCNF_X2) ),
inference(subst,[],[refute_0_2:[bind(Y1,$fot(skolemFOFtoCNF_X2)),bind(Y2,$fot(skolemFOFtoCNF_X2))]]) ).
cnf(refute_0_4,plain,
big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
~ big_f(skolemFOFtoCNF_X2,skolemFOFtoCNF_X2),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ big_f(Y1,skolemFOFtoCNF_X2)
| ~ big_g(skolemFOFtoCNF_X2,skolemFOFtoCNF_Z(Y1,skolemFOFtoCNF_X2)) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X2,skolemFOFtoCNF_X2) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)
| ~ big_g(skolemFOFtoCNF_X2,skolemFOFtoCNF_Z(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) ),
inference(subst,[],[refute_0_6:[bind(Y1,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_8,plain,
( ~ big_f(Y1,Y2)
| big_f(skolemFOFtoCNF_X2,Y2)
| big_g(Y2,skolemFOFtoCNF_Z(Y1,Y2))
| big_g(skolemFOFtoCNF_X2,skolemFOFtoCNF_Z(Y1,Y2)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_9,plain,
( ~ big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)
| big_f(skolemFOFtoCNF_X2,skolemFOFtoCNF_X2)
| big_g(skolemFOFtoCNF_X2,skolemFOFtoCNF_Z(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) ),
inference(subst,[],[refute_0_8:[bind(Y1,$fot(skolemFOFtoCNF_X1)),bind(Y2,$fot(skolemFOFtoCNF_X2))]]) ).
cnf(refute_0_10,plain,
( big_f(skolemFOFtoCNF_X2,skolemFOFtoCNF_X2)
| big_g(skolemFOFtoCNF_X2,skolemFOFtoCNF_Z(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2) )],[refute_0_4,refute_0_9]) ).
cnf(refute_0_11,plain,
big_g(skolemFOFtoCNF_X2,skolemFOFtoCNF_Z(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X2,skolemFOFtoCNF_X2) )],[refute_0_10,refute_0_5]) ).
cnf(refute_0_12,plain,
~ big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2),
inference(resolve,[$cnf( big_g(skolemFOFtoCNF_X2,skolemFOFtoCNF_Z(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2)) )],[refute_0_11,refute_0_7]) ).
cnf(refute_0_13,plain,
$false,
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X1,skolemFOFtoCNF_X2) )],[refute_0_4,refute_0_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN354+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 12 07:09:54 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
%------------------------------------------------------------------------------