TSTP Solution File: NUM341+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM341+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 : Mon Jul 18 12:26:02 EDT 2022
% Result : Theorem 0.47s 0.70s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 30 ( 8 unt; 0 def)
% Number of atoms : 66 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 63 ( 27 ~; 20 |; 8 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 87 ( 21 sgn 33 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(minus_entry_point,axiom,
! [X,Y,Z] :
( sum(Y,Z,X)
<=> difference(X,Y,Z) ) ).
fof(add_same_as_subtract,conjecture,
? [X,Y,Z] :
( sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) ) ).
fof(subgoal_0,plain,
? [X,Y,Z] :
( sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) ),
inference(strip,[],[add_same_as_subtract]) ).
fof(negate_0_0,plain,
~ ? [X,Y,Z] :
( sum(X,Y,Z)
<=> ( difference(Z,Y,X)
& difference(Z,X,Y) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y,Z] :
( ~ sum(X,Y,Z)
<=> ( difference(Z,X,Y)
& difference(Z,Y,X) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X,Y,Z] :
( ~ sum(X,Y,Z)
<=> ( difference(Z,X,Y)
& difference(Z,Y,X) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y,Z] :
( ( difference(Z,X,Y)
| sum(X,Y,Z) )
& ( difference(Z,Y,X)
| sum(X,Y,Z) )
& ( ~ difference(Z,X,Y)
| ~ difference(Z,Y,X)
| ~ sum(X,Y,Z) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y,Z] :
( ~ difference(Z,X,Y)
| ~ difference(Z,Y,X)
| ~ sum(X,Y,Z) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y,Z] :
( ~ difference(X,Y,Z)
<=> ~ sum(Y,Z,X) ),
inference(canonicalize,[],[minus_entry_point]) ).
fof(normalize_0_5,plain,
! [X,Y,Z] :
( ~ difference(X,Y,Z)
<=> ~ sum(Y,Z,X) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y,Z] :
( ( ~ difference(X,Y,Z)
| sum(Y,Z,X) )
& ( ~ sum(Y,Z,X)
| difference(X,Y,Z) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y,Z] :
( ~ sum(Y,Z,X)
| difference(X,Y,Z) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y,Z] :
( difference(Z,X,Y)
| sum(X,Y,Z) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_9,plain,
! [X,Y,Z] :
( ~ difference(X,Y,Z)
| sum(Y,Z,X) ),
inference(conjunct,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
( ~ difference(Z,X,Y)
| ~ difference(Z,Y,X)
| ~ sum(X,Y,Z) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ sum(Y,Z,X)
| difference(X,Y,Z) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_2,plain,
( ~ sum(X_118,X_119,X_120)
| difference(X_120,X_118,X_119) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_120)),bind(Y,$fot(X_118)),bind(Z,$fot(X_119))]]) ).
cnf(refute_0_3,plain,
( difference(Z,X,Y)
| sum(X,Y,Z) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_4,plain,
( difference(X_120,X_118,X_119)
| sum(X_118,X_119,X_120) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_118)),bind(Y,$fot(X_119)),bind(Z,$fot(X_120))]]) ).
cnf(refute_0_5,plain,
difference(X_120,X_118,X_119),
inference(resolve,[$cnf( sum(X_118,X_119,X_120) )],[refute_0_4,refute_0_2]) ).
cnf(refute_0_6,plain,
difference(Z,X,Y),
inference(subst,[],[refute_0_5:[bind(X_118,$fot(X)),bind(X_119,$fot(Y)),bind(X_120,$fot(Z))]]) ).
cnf(refute_0_7,plain,
( ~ difference(Z,Y,X)
| ~ sum(X,Y,Z) ),
inference(resolve,[$cnf( difference(Z,X,Y) )],[refute_0_6,refute_0_0]) ).
cnf(refute_0_8,plain,
difference(Z,Y,X),
inference(subst,[],[refute_0_5:[bind(X_118,$fot(Y)),bind(X_119,$fot(X)),bind(X_120,$fot(Z))]]) ).
cnf(refute_0_9,plain,
~ sum(X,Y,Z),
inference(resolve,[$cnf( difference(Z,Y,X) )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
( ~ difference(X,Y,Z)
| sum(Y,Z,X) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_11,plain,
( ~ difference(X_123,X_121,X_122)
| sum(X_121,X_122,X_123) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(X_123)),bind(Y,$fot(X_121)),bind(Z,$fot(X_122))]]) ).
cnf(refute_0_12,plain,
difference(X_123,X_121,X_122),
inference(subst,[],[refute_0_5:[bind(X_118,$fot(X_121)),bind(X_119,$fot(X_122)),bind(X_120,$fot(X_123))]]) ).
cnf(refute_0_13,plain,
sum(X_121,X_122,X_123),
inference(resolve,[$cnf( difference(X_123,X_121,X_122) )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
sum(X,Y,Z),
inference(subst,[],[refute_0_13:[bind(X_121,$fot(X)),bind(X_122,$fot(Y)),bind(X_123,$fot(Z))]]) ).
cnf(refute_0_15,plain,
$false,
inference(resolve,[$cnf( sum(X,Y,Z) )],[refute_0_14,refute_0_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM341+1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n020.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 : Thu Jul 7 17:59:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.47/0.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.47/0.70
% 0.47/0.70 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.54/0.70
%------------------------------------------------------------------------------