TSTP Solution File: SYN331+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN331+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 09:01:23 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 76 ( 23 ~; 18 |; 16 &)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 47 ( 5 sgn 19 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_14_3,conjecture,
? [X,Y] :
! [Z] :
( big_f(X,Z)
=> ( big_f(Y,Z)
=> ( ( big_f(X,Y)
<=> big_f(Z,Z) )
=> ( ( big_f(Y,X)
| big_f(Z,Z) )
=> ( big_f(Z,X)
| big_f(Z,Y) ) ) ) ) ) ).
fof(subgoal_0,plain,
? [X,Y] :
! [Z] :
( big_f(X,Z)
=> ( big_f(Y,Z)
=> ( ( big_f(X,Y)
<=> big_f(Z,Z) )
=> ( ( big_f(Y,X)
| big_f(Z,Z) )
=> ( big_f(Z,X)
| big_f(Z,Y) ) ) ) ) ),
inference(strip,[],[church_46_14_3]) ).
fof(negate_0_0,plain,
~ ? [X,Y] :
! [Z] :
( big_f(X,Z)
=> ( big_f(Y,Z)
=> ( ( big_f(X,Y)
<=> big_f(Z,Z) )
=> ( ( big_f(Y,X)
| big_f(Z,Z) )
=> ( big_f(Z,X)
| big_f(Z,Y) ) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
? [Z] :
( ~ big_f(Z,X)
& ~ big_f(Z,Y)
& big_f(X,Z)
& big_f(Y,Z)
& ( big_f(Y,X)
| big_f(Z,Z) )
& ( ~ big_f(X,Y)
<=> ~ big_f(Z,Z) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X,Y] :
? [Z] :
( ~ big_f(Z,X)
& ~ big_f(Z,Y)
& big_f(X,Z)
& big_f(Y,Z)
& ( big_f(Y,X)
| big_f(Z,Z) )
& ( ~ big_f(X,Y)
<=> ~ big_f(Z,Z) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ~ big_f(skolemFOFtoCNF_Z(X,Y),X)
& ~ big_f(skolemFOFtoCNF_Z(X,Y),Y)
& big_f(X,skolemFOFtoCNF_Z(X,Y))
& big_f(Y,skolemFOFtoCNF_Z(X,Y))
& ( big_f(Y,X)
| big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y)) )
& ( ~ big_f(X,Y)
<=> ~ big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y)) ) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] : ~ big_f(skolemFOFtoCNF_Z(X,Y),Y),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ big_f(X,Y)
<=> ~ big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ( ~ big_f(X,Y)
| big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y)) )
& ( ~ big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y))
| big_f(X,Y) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y))
| big_f(X,Y) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( big_f(Y,X)
| big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y)) ),
inference(conjunct,[],[normalize_0_2]) ).
cnf(refute_0_0,plain,
~ big_f(skolemFOFtoCNF_Z(X,Y),Y),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
~ big_f(skolemFOFtoCNF_Z(X,X_20),X_20),
inference(subst,[],[refute_0_0:[bind(Y,$fot(X_20))]]) ).
cnf(refute_0_2,plain,
( ~ big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y))
| big_f(X,Y) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( big_f(Y,X)
| big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
( big_f(X_17,X_16)
| big_f(skolemFOFtoCNF_Z(X_16,X_17),skolemFOFtoCNF_Z(X_16,X_17)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_16)),bind(Y,$fot(X_17))]]) ).
cnf(refute_0_5,plain,
( ~ big_f(skolemFOFtoCNF_Z(X_16,X_17),skolemFOFtoCNF_Z(X_16,X_17))
| big_f(X_16,X_17) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_16)),bind(Y,$fot(X_17))]]) ).
cnf(refute_0_6,plain,
( big_f(X_16,X_17)
| big_f(X_17,X_16) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z(X_16,X_17),skolemFOFtoCNF_Z(X_16,X_17)) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y)),
inference(subst,[],[refute_0_6:[bind(X_16,$fot(skolemFOFtoCNF_Z(X,Y))),bind(X_17,$fot(skolemFOFtoCNF_Z(X,Y)))]]) ).
cnf(refute_0_8,plain,
big_f(X,Y),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y)) )],[refute_0_7,refute_0_2]) ).
cnf(refute_0_9,plain,
big_f(skolemFOFtoCNF_Z(X,X_20),X_20),
inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_Z(X,X_20))),bind(Y,$fot(X_20))]]) ).
cnf(refute_0_10,plain,
$false,
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z(X,X_20),X_20) )],[refute_0_9,refute_0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN331+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n017.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 19:19:34 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
%------------------------------------------------------------------------------