TSTP Solution File: SYN356+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN356+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 09:01:43 EDT 2022
% Result : Theorem 0.21s 0.36s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 47 ( 15 unt; 0 def)
% Number of atoms : 126 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 118 ( 39 ~; 31 |; 33 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 68 ( 2 sgn 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2107,conjecture,
( ( big_r(a,b)
& ! [X,Y] :
( big_r(X,Y)
=> ( big_r(Y,X)
& big_q(X,Y) ) )
& ! [U,V] :
( big_q(U,V)
=> big_q(U,U) ) )
=> ( big_q(a,a)
& big_q(b,b) ) ) ).
fof(subgoal_0,plain,
( ( big_r(a,b)
& ! [X,Y] :
( big_r(X,Y)
=> ( big_r(Y,X)
& big_q(X,Y) ) )
& ! [U,V] :
( big_q(U,V)
=> big_q(U,U) ) )
=> big_q(a,a) ),
inference(strip,[],[x2107]) ).
fof(subgoal_1,plain,
( ( big_r(a,b)
& ! [X,Y] :
( big_r(X,Y)
=> ( big_r(Y,X)
& big_q(X,Y) ) )
& ! [U,V] :
( big_q(U,V)
=> big_q(U,U) )
& big_q(a,a) )
=> big_q(b,b) ),
inference(strip,[],[x2107]) ).
fof(negate_0_0,plain,
~ ( ( big_r(a,b)
& ! [X,Y] :
( big_r(X,Y)
=> ( big_r(Y,X)
& big_q(X,Y) ) )
& ! [U,V] :
( big_q(U,V)
=> big_q(U,U) ) )
=> big_q(a,a) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ big_q(a,a)
& big_r(a,b)
& ! [U] :
( big_q(U,U)
| ! [V] : ~ big_q(U,V) )
& ! [X,Y] :
( ~ big_r(X,Y)
| ( big_q(X,Y)
& big_r(Y,X) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [U] :
( big_q(U,U)
| ! [V] : ~ big_q(U,V) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [U] :
( big_q(U,U)
| ! [V] : ~ big_q(U,V) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [U,V] :
( ~ big_q(U,V)
| big_q(U,U) ),
inference(clausify,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
big_r(a,b),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ big_r(X,Y)
| ( big_q(X,Y)
& big_r(Y,X) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ big_r(X,Y)
| ( big_q(X,Y)
& big_r(Y,X) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ( ~ big_r(X,Y)
| big_q(X,Y) )
& ( ~ big_r(X,Y)
| big_r(Y,X) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ big_r(X,Y)
| big_q(X,Y) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
~ big_q(a,a),
inference(conjunct,[],[normalize_0_0]) ).
cnf(refute_0_0,plain,
( ~ big_q(U,V)
| big_q(U,U) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ big_q(a,b)
| big_q(a,a) ),
inference(subst,[],[refute_0_0:[bind(U,$fot(a)),bind(V,$fot(b))]]) ).
cnf(refute_0_2,plain,
big_r(a,b),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( ~ big_r(X,Y)
| big_q(X,Y) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_4,plain,
( ~ big_r(a,b)
| big_q(a,b) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_5,plain,
big_q(a,b),
inference(resolve,[$cnf( big_r(a,b) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
big_q(a,a),
inference(resolve,[$cnf( big_q(a,b) )],[refute_0_5,refute_0_1]) ).
cnf(refute_0_7,plain,
~ big_q(a,a),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
$false,
inference(resolve,[$cnf( big_q(a,a) )],[refute_0_6,refute_0_7]) ).
fof(negate_1_0,plain,
~ ( ( big_r(a,b)
& ! [X,Y] :
( big_r(X,Y)
=> ( big_r(Y,X)
& big_q(X,Y) ) )
& ! [U,V] :
( big_q(U,V)
=> big_q(U,U) )
& big_q(a,a) )
=> big_q(b,b) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
( ~ big_q(b,b)
& big_q(a,a)
& big_r(a,b)
& ! [U] :
( big_q(U,U)
| ! [V] : ~ big_q(U,V) )
& ! [X,Y] :
( ~ big_r(X,Y)
| ( big_q(X,Y)
& big_r(Y,X) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
! [U] :
( big_q(U,U)
| ! [V] : ~ big_q(U,V) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [U] :
( big_q(U,U)
| ! [V] : ~ big_q(U,V) ),
inference(specialize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [U,V] :
( ~ big_q(U,V)
| big_q(U,U) ),
inference(clausify,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [X,Y] :
( ~ big_r(X,Y)
| ( big_q(X,Y)
& big_r(Y,X) ) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_5,plain,
! [X,Y] :
( ~ big_r(X,Y)
| ( big_q(X,Y)
& big_r(Y,X) ) ),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [X,Y] :
( ( ~ big_r(X,Y)
| big_q(X,Y) )
& ( ~ big_r(X,Y)
| big_r(Y,X) ) ),
inference(clausify,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [X,Y] :
( ~ big_r(X,Y)
| big_q(X,Y) ),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
big_r(a,b),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_9,plain,
! [X,Y] :
( ~ big_r(X,Y)
| big_r(Y,X) ),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_10,plain,
~ big_q(b,b),
inference(conjunct,[],[normalize_1_0]) ).
cnf(refute_1_0,plain,
( ~ big_q(U,V)
| big_q(U,U) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( ~ big_q(b,a)
| big_q(b,b) ),
inference(subst,[],[refute_1_0:[bind(U,$fot(b)),bind(V,$fot(a))]]) ).
cnf(refute_1_2,plain,
( ~ big_r(X,Y)
| big_q(X,Y) ),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_3,plain,
( ~ big_r(b,a)
| big_q(b,a) ),
inference(subst,[],[refute_1_2:[bind(X,$fot(b)),bind(Y,$fot(a))]]) ).
cnf(refute_1_4,plain,
big_r(a,b),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_5,plain,
( ~ big_r(X,Y)
| big_r(Y,X) ),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_6,plain,
( ~ big_r(a,b)
| big_r(b,a) ),
inference(subst,[],[refute_1_5:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_1_7,plain,
big_r(b,a),
inference(resolve,[$cnf( big_r(a,b) )],[refute_1_4,refute_1_6]) ).
cnf(refute_1_8,plain,
big_q(b,a),
inference(resolve,[$cnf( big_r(b,a) )],[refute_1_7,refute_1_3]) ).
cnf(refute_1_9,plain,
big_q(b,b),
inference(resolve,[$cnf( big_q(b,a) )],[refute_1_8,refute_1_1]) ).
cnf(refute_1_10,plain,
~ big_q(b,b),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_11,plain,
$false,
inference(resolve,[$cnf( big_q(b,b) )],[refute_1_9,refute_1_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SYN356+1 : TPTP v8.1.0. Released v2.0.0.
% 0.13/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jul 12 03:14:29 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.36
% 0.21/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.21/0.36
%------------------------------------------------------------------------------