TSTP Solution File: SYN332+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN332+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 09:01:24 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 1
% Syntax : Number of formulae : 55 ( 8 unt; 0 def)
% Number of atoms : 203 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 237 ( 89 ~; 59 |; 32 &)
% ( 42 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 110 ( 9 sgn 41 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_14_4,conjecture,
? [X,Y] :
! [Z] :
( ~ ( ( big_f(X,Y)
& big_f(Y,X) )
<=> big_f(X,Z) )
=> ( ( big_f(X,Z)
<=> big_f(Z,X) )
=> ( ( big_f(X,Z)
<=> big_f(Y,Z) )
=> ( ( ( big_f(Y,X)
=> big_f(X,Y) )
<=> big_f(Z,Z) )
=> ( ( big_f(X,Y)
<=> big_f(Y,X) )
<=> big_f(Z,Y) ) ) ) ) ) ).
fof(subgoal_0,plain,
? [X,Y] :
! [Z] :
( ~ ( ( big_f(X,Y)
& big_f(Y,X) )
<=> big_f(X,Z) )
=> ( ( big_f(X,Z)
<=> big_f(Z,X) )
=> ( ( big_f(X,Z)
<=> big_f(Y,Z) )
=> ( ( ( big_f(Y,X)
=> big_f(X,Y) )
<=> big_f(Z,Z) )
=> ( ( big_f(X,Y)
<=> big_f(Y,X) )
<=> big_f(Z,Y) ) ) ) ) ),
inference(strip,[],[church_46_14_4]) ).
fof(negate_0_0,plain,
~ ? [X,Y] :
! [Z] :
( ~ ( ( big_f(X,Y)
& big_f(Y,X) )
<=> big_f(X,Z) )
=> ( ( big_f(X,Z)
<=> big_f(Z,X) )
=> ( ( big_f(X,Z)
<=> big_f(Y,Z) )
=> ( ( ( big_f(Y,X)
=> big_f(X,Y) )
<=> big_f(Z,Z) )
=> ( ( big_f(X,Y)
<=> big_f(Y,X) )
<=> big_f(Z,Y) ) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
? [Z] :
( ( ~ big_f(X,Z)
<=> ~ big_f(Y,Z) )
& ( ~ big_f(X,Z)
<=> ~ big_f(Z,X) )
& ( ~ big_f(X,Z)
<=> ( big_f(X,Y)
& big_f(Y,X) ) )
& ( ~ big_f(Z,Z)
<=> ( ~ big_f(X,Y)
& big_f(Y,X) ) )
& ( ~ big_f(X,Y)
<=> ( ~ big_f(Y,X)
<=> ~ big_f(Z,Y) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X,Y] :
? [Z] :
( ( ~ big_f(X,Z)
<=> ~ big_f(Y,Z) )
& ( ~ big_f(X,Z)
<=> ~ big_f(Z,X) )
& ( ~ big_f(X,Z)
<=> ( big_f(X,Y)
& big_f(Y,X) ) )
& ( ~ big_f(Z,Z)
<=> ( ~ big_f(X,Y)
& big_f(Y,X) ) )
& ( ~ big_f(X,Y)
<=> ( ~ big_f(Y,X)
<=> ~ big_f(Z,Y) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ( ~ big_f(X,skolemFOFtoCNF_Z(X,Y))
<=> ~ big_f(Y,skolemFOFtoCNF_Z(X,Y)) )
& ( ~ big_f(X,skolemFOFtoCNF_Z(X,Y))
<=> ~ big_f(skolemFOFtoCNF_Z(X,Y),X) )
& ( ~ big_f(X,skolemFOFtoCNF_Z(X,Y))
<=> ( big_f(X,Y)
& big_f(Y,X) ) )
& ( ~ big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y))
<=> ( ~ big_f(X,Y)
& big_f(Y,X) ) )
& ( ~ big_f(X,Y)
<=> ( ~ big_f(Y,X)
<=> ~ big_f(skolemFOFtoCNF_Z(X,Y),Y) ) ) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ big_f(X,Y)
<=> ( ~ big_f(Y,X)
<=> ~ 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(Y,X)
| ~ big_f(skolemFOFtoCNF_Z(X,Y),Y) )
& ( ~ big_f(X,Y)
| big_f(Y,X)
| big_f(skolemFOFtoCNF_Z(X,Y),Y) )
& ( ~ big_f(Y,X)
| big_f(X,Y)
| big_f(skolemFOFtoCNF_Z(X,Y),Y) )
& ( ~ big_f(skolemFOFtoCNF_Z(X,Y),Y)
| big_f(X,Y)
| big_f(Y,X) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ big_f(X,Y)
| ~ big_f(Y,X)
| ~ big_f(skolemFOFtoCNF_Z(X,Y),Y) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y))
<=> ( ~ big_f(X,Y)
& big_f(Y,X) ) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ( ~ big_f(X,Y)
| big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y)) )
& ( big_f(Y,X)
| big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y)) )
& ( ~ big_f(Y,X)
| ~ big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y))
| big_f(X,Y) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ big_f(Y,X)
| ~ big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y))
| big_f(X,Y) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ big_f(X,skolemFOFtoCNF_Z(X,Y))
<=> ( big_f(X,Y)
& big_f(Y,X) ) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ( big_f(X,Y)
| big_f(X,skolemFOFtoCNF_Z(X,Y)) )
& ( big_f(X,skolemFOFtoCNF_Z(X,Y))
| big_f(Y,X) )
& ( ~ big_f(X,Y)
| ~ big_f(X,skolemFOFtoCNF_Z(X,Y))
| ~ big_f(Y,X) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( big_f(X,skolemFOFtoCNF_Z(X,Y))
| big_f(Y,X) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ big_f(X,skolemFOFtoCNF_Z(X,Y))
<=> ~ big_f(skolemFOFtoCNF_Z(X,Y),X) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ( ~ big_f(X,skolemFOFtoCNF_Z(X,Y))
| big_f(skolemFOFtoCNF_Z(X,Y),X) )
& ( ~ big_f(skolemFOFtoCNF_Z(X,Y),X)
| big_f(X,skolemFOFtoCNF_Z(X,Y)) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ big_f(X,skolemFOFtoCNF_Z(X,Y))
| big_f(skolemFOFtoCNF_Z(X,Y),X) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ big_f(skolemFOFtoCNF_Z(X,Y),Y)
| big_f(X,Y)
| big_f(Y,X) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ~ big_f(X,skolemFOFtoCNF_Z(X,Y))
<=> ~ big_f(Y,skolemFOFtoCNF_Z(X,Y)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_17,plain,
! [X,Y] :
( ( ~ big_f(X,skolemFOFtoCNF_Z(X,Y))
| big_f(Y,skolemFOFtoCNF_Z(X,Y)) )
& ( ~ big_f(Y,skolemFOFtoCNF_Z(X,Y))
| big_f(X,skolemFOFtoCNF_Z(X,Y)) ) ),
inference(clausify,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X,Y] :
( ~ big_f(X,skolemFOFtoCNF_Z(X,Y))
| big_f(Y,skolemFOFtoCNF_Z(X,Y)) ),
inference(conjunct,[],[normalize_0_17]) ).
cnf(refute_0_0,plain,
( ~ big_f(X,Y)
| ~ big_f(Y,X)
| ~ big_f(skolemFOFtoCNF_Z(X,Y),Y) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_1,plain,
( ~ big_f(X,X_44)
| ~ big_f(X_44,X)
| ~ big_f(skolemFOFtoCNF_Z(X,X_44),X_44) ),
inference(subst,[],[refute_0_0:[bind(Y,$fot(X_44))]]) ).
cnf(refute_0_2,plain,
( ~ big_f(Y,X)
| ~ big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y))
| big_f(X,Y) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_3,plain,
( big_f(X,skolemFOFtoCNF_Z(X,Y))
| big_f(Y,X) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_4,plain,
( big_f(X_12,skolemFOFtoCNF_Z(X_12,X_13))
| big_f(X_13,X_12) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_12)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_5,plain,
( ~ big_f(X,skolemFOFtoCNF_Z(X,Y))
| big_f(skolemFOFtoCNF_Z(X,Y),X) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_6,plain,
( ~ big_f(X_12,skolemFOFtoCNF_Z(X_12,X_13))
| big_f(skolemFOFtoCNF_Z(X_12,X_13),X_12) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_12)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_7,plain,
( big_f(X_13,X_12)
| big_f(skolemFOFtoCNF_Z(X_12,X_13),X_12) ),
inference(resolve,[$cnf( big_f(X_12,skolemFOFtoCNF_Z(X_12,X_13)) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( big_f(X_36,X_36)
| big_f(skolemFOFtoCNF_Z(X_36,X_36),X_36) ),
inference(subst,[],[refute_0_7:[bind(X_12,$fot(X_36)),bind(X_13,$fot(X_36))]]) ).
cnf(refute_0_9,plain,
( ~ big_f(skolemFOFtoCNF_Z(X,Y),Y)
| big_f(X,Y)
| big_f(Y,X) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_10,plain,
( ~ big_f(skolemFOFtoCNF_Z(X_36,X_36),X_36)
| big_f(X_36,X_36) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_36)),bind(Y,$fot(X_36))]]) ).
cnf(refute_0_11,plain,
big_f(X_36,X_36),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z(X_36,X_36),X_36) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y)),
inference(subst,[],[refute_0_11:[bind(X_36,$fot(skolemFOFtoCNF_Z(X,Y)))]]) ).
cnf(refute_0_13,plain,
( ~ big_f(Y,X)
| big_f(X,Y) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z(X,Y),skolemFOFtoCNF_Z(X,Y)) )],[refute_0_12,refute_0_2]) ).
cnf(refute_0_14,plain,
( ~ big_f(X_42,X_43)
| big_f(X_43,X_42) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_43)),bind(Y,$fot(X_42))]]) ).
cnf(refute_0_15,plain,
( ~ big_f(skolemFOFtoCNF_Z(X_41,X_40),X_40)
| big_f(X_40,X_41)
| big_f(X_41,X_40) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_41)),bind(Y,$fot(X_40))]]) ).
cnf(refute_0_16,plain,
( ~ big_f(X,skolemFOFtoCNF_Z(X,Y))
| big_f(Y,skolemFOFtoCNF_Z(X,Y)) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_17,plain,
( ~ big_f(X_6,skolemFOFtoCNF_Z(X_6,X_7))
| big_f(X_7,skolemFOFtoCNF_Z(X_6,X_7)) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(X_6)),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_18,plain,
( big_f(X_6,skolemFOFtoCNF_Z(X_6,X_7))
| big_f(X_7,X_6) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_6)),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_19,plain,
( big_f(X_7,X_6)
| big_f(X_7,skolemFOFtoCNF_Z(X_6,X_7)) ),
inference(resolve,[$cnf( big_f(X_6,skolemFOFtoCNF_Z(X_6,X_7)) )],[refute_0_18,refute_0_17]) ).
cnf(refute_0_20,plain,
( big_f(X_39,X_6)
| big_f(X_39,skolemFOFtoCNF_Z(X_6,X_39)) ),
inference(subst,[],[refute_0_19:[bind(X_7,$fot(X_39))]]) ).
cnf(refute_0_21,plain,
( ~ big_f(X_39,skolemFOFtoCNF_Z(X_6,X_39))
| big_f(skolemFOFtoCNF_Z(X_6,X_39),X_39) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(skolemFOFtoCNF_Z(X_6,X_39))),bind(Y,$fot(X_39))]]) ).
cnf(refute_0_22,plain,
( big_f(X_39,X_6)
| big_f(skolemFOFtoCNF_Z(X_6,X_39),X_39) ),
inference(resolve,[$cnf( big_f(X_39,skolemFOFtoCNF_Z(X_6,X_39)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( big_f(X_40,X_41)
| big_f(skolemFOFtoCNF_Z(X_41,X_40),X_40) ),
inference(subst,[],[refute_0_22:[bind(X_39,$fot(X_40)),bind(X_6,$fot(X_41))]]) ).
cnf(refute_0_24,plain,
( big_f(X_40,X_41)
| big_f(X_41,X_40) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z(X_41,X_40),X_40) )],[refute_0_23,refute_0_15]) ).
cnf(refute_0_25,plain,
( big_f(X_42,X_43)
| big_f(X_43,X_42) ),
inference(subst,[],[refute_0_24:[bind(X_40,$fot(X_43)),bind(X_41,$fot(X_42))]]) ).
cnf(refute_0_26,plain,
big_f(X_43,X_42),
inference(resolve,[$cnf( big_f(X_42,X_43) )],[refute_0_25,refute_0_14]) ).
cnf(refute_0_27,plain,
big_f(skolemFOFtoCNF_Z(X,X_44),X_44),
inference(subst,[],[refute_0_26:[bind(X_42,$fot(X_44)),bind(X_43,$fot(skolemFOFtoCNF_Z(X,X_44)))]]) ).
cnf(refute_0_28,plain,
( ~ big_f(X,X_44)
| ~ big_f(X_44,X) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_Z(X,X_44),X_44) )],[refute_0_27,refute_0_1]) ).
cnf(refute_0_29,plain,
big_f(X,X_44),
inference(subst,[],[refute_0_26:[bind(X_42,$fot(X_44)),bind(X_43,$fot(X))]]) ).
cnf(refute_0_30,plain,
~ big_f(X_44,X),
inference(resolve,[$cnf( big_f(X,X_44) )],[refute_0_29,refute_0_28]) ).
cnf(refute_0_31,plain,
big_f(X_44,X),
inference(subst,[],[refute_0_26:[bind(X_42,$fot(X)),bind(X_43,$fot(X_44))]]) ).
cnf(refute_0_32,plain,
$false,
inference(resolve,[$cnf( big_f(X_44,X) )],[refute_0_31,refute_0_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN332+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n019.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 : Tue Jul 12 04:29:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36
%------------------------------------------------------------------------------