TSTP Solution File: SYN059+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN059+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 08:59:06 EDT 2022
% Result : Theorem 0.14s 0.35s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 77 ( 33 unt; 0 def)
% Number of atoms : 218 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 215 ( 74 ~; 48 |; 59 &)
% ( 1 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-1 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 91 ( 5 sgn 63 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel29_1,axiom,
? [X] : big_f(X) ).
fof(pel29_2,axiom,
? [Y] : big_g(Y) ).
fof(pel29,conjecture,
( ( ! [X] :
( big_f(X)
=> big_h(X) )
& ! [U] :
( big_g(U)
=> big_j(U) ) )
<=> ! [W,Y] :
( ( big_f(W)
& big_g(Y) )
=> ( big_h(W)
& big_j(Y) ) ) ) ).
fof(subgoal_0,plain,
( ( ! [X] :
( big_f(X)
=> big_h(X) )
& ! [U] :
( big_g(U)
=> big_j(U) ) )
=> ! [W,Y] :
( ( big_f(W)
& big_g(Y) )
=> big_h(W) ) ),
inference(strip,[],[pel29]) ).
fof(subgoal_1,plain,
( ( ! [X] :
( big_f(X)
=> big_h(X) )
& ! [U] :
( big_g(U)
=> big_j(U) ) )
=> ! [W,Y] :
( ( big_f(W)
& big_g(Y)
& big_h(W) )
=> big_j(Y) ) ),
inference(strip,[],[pel29]) ).
fof(subgoal_2,plain,
( ! [W,Y] :
( ( big_f(W)
& big_g(Y) )
=> ( big_h(W)
& big_j(Y) ) )
=> ! [X] :
( big_f(X)
=> big_h(X) ) ),
inference(strip,[],[pel29]) ).
fof(subgoal_3,plain,
( ( ! [W,Y] :
( ( big_f(W)
& big_g(Y) )
=> ( big_h(W)
& big_j(Y) ) )
& ! [X] :
( big_f(X)
=> big_h(X) ) )
=> ! [U] :
( big_g(U)
=> big_j(U) ) ),
inference(strip,[],[pel29]) ).
fof(negate_0_0,plain,
~ ( ( ! [X] :
( big_f(X)
=> big_h(X) )
& ! [U] :
( big_g(U)
=> big_j(U) ) )
=> ! [W,Y] :
( ( big_f(W)
& big_g(Y) )
=> big_h(W) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ? [W] :
( ~ big_h(W)
& big_f(W)
& ? [Y] : big_g(Y) )
& ! [U] :
( ~ big_g(U)
| big_j(U) )
& ! [X] :
( ~ big_f(X)
| big_h(X) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
? [W] :
( ~ big_h(W)
& big_f(W)
& ? [Y] : big_g(Y) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ big_h(skolemFOFtoCNF_W)
& big_f(skolemFOFtoCNF_W)
& ? [Y] : big_g(Y) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
big_f(skolemFOFtoCNF_W),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] :
( ~ big_f(X)
| big_h(X) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_5,plain,
! [X] :
( ~ big_f(X)
| big_h(X) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
~ big_h(skolemFOFtoCNF_W),
inference(conjunct,[],[normalize_0_2]) ).
cnf(refute_0_0,plain,
big_f(skolemFOFtoCNF_W),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ big_f(X)
| big_h(X) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ big_f(skolemFOFtoCNF_W)
| big_h(skolemFOFtoCNF_W) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_3,plain,
big_h(skolemFOFtoCNF_W),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_W) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
~ big_h(skolemFOFtoCNF_W),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
$false,
inference(resolve,[$cnf( big_h(skolemFOFtoCNF_W) )],[refute_0_3,refute_0_4]) ).
fof(negate_1_0,plain,
~ ( ( ! [X] :
( big_f(X)
=> big_h(X) )
& ! [U] :
( big_g(U)
=> big_j(U) ) )
=> ! [W,Y] :
( ( big_f(W)
& big_g(Y)
& big_h(W) )
=> big_j(Y) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
( ? [W,Y] :
( ~ big_j(Y)
& big_f(W)
& big_g(Y)
& big_h(W) )
& ! [U] :
( ~ big_g(U)
| big_j(U) )
& ! [X] :
( ~ big_f(X)
| big_h(X) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
? [W,Y] :
( ~ big_j(Y)
& big_f(W)
& big_g(Y)
& big_h(W) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
( ~ big_j(skolemFOFtoCNF_Y_2)
& big_f(skolemFOFtoCNF_W_1)
& big_g(skolemFOFtoCNF_Y_2)
& big_h(skolemFOFtoCNF_W_1) ),
inference(skolemize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
big_g(skolemFOFtoCNF_Y_2),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [U] :
( ~ big_g(U)
| big_j(U) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_5,plain,
! [U] :
( ~ big_g(U)
| big_j(U) ),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
~ big_j(skolemFOFtoCNF_Y_2),
inference(conjunct,[],[normalize_1_2]) ).
cnf(refute_1_0,plain,
big_g(skolemFOFtoCNF_Y_2),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( ~ big_g(U)
| big_j(U) ),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_2,plain,
( ~ big_g(skolemFOFtoCNF_Y_2)
| big_j(skolemFOFtoCNF_Y_2) ),
inference(subst,[],[refute_1_1:[bind(U,$fot(skolemFOFtoCNF_Y_2))]]) ).
cnf(refute_1_3,plain,
big_j(skolemFOFtoCNF_Y_2),
inference(resolve,[$cnf( big_g(skolemFOFtoCNF_Y_2) )],[refute_1_0,refute_1_2]) ).
cnf(refute_1_4,plain,
~ big_j(skolemFOFtoCNF_Y_2),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_5,plain,
$false,
inference(resolve,[$cnf( big_j(skolemFOFtoCNF_Y_2) )],[refute_1_3,refute_1_4]) ).
fof(negate_2_0,plain,
~ ( ! [W,Y] :
( ( big_f(W)
& big_g(Y) )
=> ( big_h(W)
& big_j(Y) ) )
=> ! [X] :
( big_f(X)
=> big_h(X) ) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
( ? [X] :
( ~ big_h(X)
& big_f(X) )
& ! [W,Y] :
( ~ big_f(W)
| ~ big_g(Y)
| ( big_h(W)
& big_j(Y) ) ) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
? [X] :
( ~ big_h(X)
& big_f(X) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
( ~ big_h(skolemFOFtoCNF_X_1)
& big_f(skolemFOFtoCNF_X_1) ),
inference(skolemize,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
big_f(skolemFOFtoCNF_X_1),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_4,plain,
? [Y] : big_g(Y),
inference(canonicalize,[],[pel29_2]) ).
fof(normalize_2_5,plain,
big_g(skolemFOFtoCNF_Y),
inference(skolemize,[],[normalize_2_4]) ).
fof(normalize_2_6,plain,
! [W,Y] :
( ~ big_f(W)
| ~ big_g(Y)
| ( big_h(W)
& big_j(Y) ) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_7,plain,
! [W,Y] :
( ~ big_f(W)
| ~ big_g(Y)
| ( big_h(W)
& big_j(Y) ) ),
inference(specialize,[],[normalize_2_6]) ).
fof(normalize_2_8,plain,
! [W,Y] :
( ( ~ big_f(W)
| ~ big_g(Y)
| big_h(W) )
& ( ~ big_f(W)
| ~ big_g(Y)
| big_j(Y) ) ),
inference(clausify,[],[normalize_2_7]) ).
fof(normalize_2_9,plain,
! [W,Y] :
( ~ big_f(W)
| ~ big_g(Y)
| big_h(W) ),
inference(conjunct,[],[normalize_2_8]) ).
fof(normalize_2_10,plain,
~ big_h(skolemFOFtoCNF_X_1),
inference(conjunct,[],[normalize_2_2]) ).
cnf(refute_2_0,plain,
big_f(skolemFOFtoCNF_X_1),
inference(canonicalize,[],[normalize_2_3]) ).
cnf(refute_2_1,plain,
big_g(skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_2_5]) ).
cnf(refute_2_2,plain,
( ~ big_f(W)
| ~ big_g(Y)
| big_h(W) ),
inference(canonicalize,[],[normalize_2_9]) ).
cnf(refute_2_3,plain,
( ~ big_f(X_2)
| ~ big_g(skolemFOFtoCNF_Y)
| big_h(X_2) ),
inference(subst,[],[refute_2_2:[bind(W,$fot(X_2)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_2_4,plain,
( ~ big_f(X_2)
| big_h(X_2) ),
inference(resolve,[$cnf( big_g(skolemFOFtoCNF_Y) )],[refute_2_1,refute_2_3]) ).
cnf(refute_2_5,plain,
( ~ big_f(skolemFOFtoCNF_X_1)
| big_h(skolemFOFtoCNF_X_1) ),
inference(subst,[],[refute_2_4:[bind(X_2,$fot(skolemFOFtoCNF_X_1))]]) ).
cnf(refute_2_6,plain,
big_h(skolemFOFtoCNF_X_1),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X_1) )],[refute_2_0,refute_2_5]) ).
cnf(refute_2_7,plain,
~ big_h(skolemFOFtoCNF_X_1),
inference(canonicalize,[],[normalize_2_10]) ).
cnf(refute_2_8,plain,
$false,
inference(resolve,[$cnf( big_h(skolemFOFtoCNF_X_1) )],[refute_2_6,refute_2_7]) ).
fof(negate_3_0,plain,
~ ( ( ! [W,Y] :
( ( big_f(W)
& big_g(Y) )
=> ( big_h(W)
& big_j(Y) ) )
& ! [X] :
( big_f(X)
=> big_h(X) ) )
=> ! [U] :
( big_g(U)
=> big_j(U) ) ),
inference(negate,[],[subgoal_3]) ).
fof(normalize_3_0,plain,
? [X] : big_f(X),
inference(canonicalize,[],[pel29_1]) ).
fof(normalize_3_1,plain,
big_f(skolemFOFtoCNF_X),
inference(skolemize,[],[normalize_3_0]) ).
fof(normalize_3_2,plain,
( ? [U] :
( ~ big_j(U)
& big_g(U) )
& ! [X] :
( ~ big_f(X)
| big_h(X) )
& ! [W,Y] :
( ~ big_f(W)
| ~ big_g(Y)
| ( big_h(W)
& big_j(Y) ) ) ),
inference(canonicalize,[],[negate_3_0]) ).
fof(normalize_3_3,plain,
? [U] :
( ~ big_j(U)
& big_g(U) ),
inference(conjunct,[],[normalize_3_2]) ).
fof(normalize_3_4,plain,
( ~ big_j(skolemFOFtoCNF_U)
& big_g(skolemFOFtoCNF_U) ),
inference(skolemize,[],[normalize_3_3]) ).
fof(normalize_3_5,plain,
big_g(skolemFOFtoCNF_U),
inference(conjunct,[],[normalize_3_4]) ).
fof(normalize_3_6,plain,
! [W,Y] :
( ~ big_f(W)
| ~ big_g(Y)
| ( big_h(W)
& big_j(Y) ) ),
inference(conjunct,[],[normalize_3_2]) ).
fof(normalize_3_7,plain,
! [W,Y] :
( ~ big_f(W)
| ~ big_g(Y)
| ( big_h(W)
& big_j(Y) ) ),
inference(specialize,[],[normalize_3_6]) ).
fof(normalize_3_8,plain,
! [W,Y] :
( ( ~ big_f(W)
| ~ big_g(Y)
| big_h(W) )
& ( ~ big_f(W)
| ~ big_g(Y)
| big_j(Y) ) ),
inference(clausify,[],[normalize_3_7]) ).
fof(normalize_3_9,plain,
! [W,Y] :
( ~ big_f(W)
| ~ big_g(Y)
| big_j(Y) ),
inference(conjunct,[],[normalize_3_8]) ).
fof(normalize_3_10,plain,
~ big_j(skolemFOFtoCNF_U),
inference(conjunct,[],[normalize_3_4]) ).
cnf(refute_3_0,plain,
big_f(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_3_1]) ).
cnf(refute_3_1,plain,
big_g(skolemFOFtoCNF_U),
inference(canonicalize,[],[normalize_3_5]) ).
cnf(refute_3_2,plain,
( ~ big_f(W)
| ~ big_g(Y)
| big_j(Y) ),
inference(canonicalize,[],[normalize_3_9]) ).
cnf(refute_3_3,plain,
( ~ big_f(X_6)
| ~ big_g(skolemFOFtoCNF_U)
| big_j(skolemFOFtoCNF_U) ),
inference(subst,[],[refute_3_2:[bind(W,$fot(X_6)),bind(Y,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_3_4,plain,
( ~ big_f(X_6)
| big_j(skolemFOFtoCNF_U) ),
inference(resolve,[$cnf( big_g(skolemFOFtoCNF_U) )],[refute_3_1,refute_3_3]) ).
cnf(refute_3_5,plain,
~ big_j(skolemFOFtoCNF_U),
inference(canonicalize,[],[normalize_3_10]) ).
cnf(refute_3_6,plain,
~ big_f(X_6),
inference(resolve,[$cnf( big_j(skolemFOFtoCNF_U) )],[refute_3_4,refute_3_5]) ).
cnf(refute_3_7,plain,
~ big_f(skolemFOFtoCNF_X),
inference(subst,[],[refute_3_6:[bind(X_6,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_3_8,plain,
$false,
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X) )],[refute_3_0,refute_3_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN059+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jul 12 00:29:40 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35
% 0.14/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.36
%------------------------------------------------------------------------------