TSTP Solution File: SYN056+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN056+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 08:59:03 EDT 2022
% Result : Theorem 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 65 ( 16 unt; 0 def)
% Number of atoms : 168 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 189 ( 86 ~; 66 |; 13 &)
% ( 9 <=>; 15 =>; 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 64 ( 2 sgn 40 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel26_1,axiom,
( ? [X] : big_p(X)
<=> ? [Y] : big_q(Y) ) ).
fof(pel26_2,axiom,
! [X,Y] :
( ( big_p(X)
& big_q(Y) )
=> ( big_r(X)
<=> big_s(Y) ) ) ).
fof(pel26,conjecture,
( ! [X] :
( big_p(X)
=> big_r(X) )
<=> ! [Y] :
( big_q(Y)
=> big_s(Y) ) ) ).
fof(subgoal_0,plain,
( ! [X] :
( big_p(X)
=> big_r(X) )
=> ! [Y] :
( big_q(Y)
=> big_s(Y) ) ),
inference(strip,[],[pel26]) ).
fof(subgoal_1,plain,
( ! [Y] :
( big_q(Y)
=> big_s(Y) )
=> ! [X] :
( big_p(X)
=> big_r(X) ) ),
inference(strip,[],[pel26]) ).
fof(negate_0_0,plain,
~ ( ! [X] :
( big_p(X)
=> big_r(X) )
=> ! [Y] :
( big_q(Y)
=> big_s(Y) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ? [Y] :
( ~ big_s(Y)
& big_q(Y) )
& ! [X] :
( ~ big_p(X)
| big_r(X) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
? [Y] :
( ~ big_s(Y)
& big_q(Y) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ big_s(skolemFOFtoCNF_Y_1)
& big_q(skolemFOFtoCNF_Y_1) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
big_q(skolemFOFtoCNF_Y_1),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
( ? [X] : big_p(X)
<=> ? [Y] : big_q(Y) ),
inference(canonicalize,[],[pel26_1]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ( ~ big_p(X)
| big_q(skolemFOFtoCNF_Y) )
& ( ~ big_q(Y)
| big_p(skolemFOFtoCNF_X) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [Y] :
( ~ big_q(Y)
| big_p(skolemFOFtoCNF_X) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X] :
( ~ big_p(X)
| big_r(X) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_8,plain,
! [X] :
( ~ big_p(X)
| big_r(X) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ big_p(X)
| ~ big_q(Y)
| ( ~ big_r(X)
<=> ~ big_s(Y) ) ),
inference(canonicalize,[],[pel26_2]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ big_p(X)
| ~ big_q(Y)
| ( ~ big_r(X)
<=> ~ big_s(Y) ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ( ~ big_p(X)
| ~ big_q(Y)
| ~ big_r(X)
| big_s(Y) )
& ( ~ big_p(X)
| ~ big_q(Y)
| ~ big_s(Y)
| big_r(X) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ big_p(X)
| ~ big_q(Y)
| ~ big_r(X)
| big_s(Y) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
~ big_s(skolemFOFtoCNF_Y_1),
inference(conjunct,[],[normalize_0_2]) ).
cnf(refute_0_0,plain,
big_q(skolemFOFtoCNF_Y_1),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ big_q(Y)
| big_p(skolemFOFtoCNF_X) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ big_q(skolemFOFtoCNF_Y_1)
| big_p(skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_1:[bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_0_3,plain,
big_p(skolemFOFtoCNF_X),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_Y_1) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ big_p(X)
| big_r(X) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ big_p(skolemFOFtoCNF_X)
| big_r(skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_6,plain,
big_r(skolemFOFtoCNF_X),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ big_p(X)
| ~ big_q(Y)
| ~ big_r(X)
| big_s(Y) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_8,plain,
( ~ big_p(skolemFOFtoCNF_X)
| ~ big_q(X_4)
| ~ big_r(skolemFOFtoCNF_X)
| big_s(X_4) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(X_4))]]) ).
cnf(refute_0_9,plain,
( ~ big_p(skolemFOFtoCNF_X)
| ~ big_q(X_4)
| big_s(X_4) ),
inference(resolve,[$cnf( big_r(skolemFOFtoCNF_X) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ big_q(X_4)
| big_s(X_4) ),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X) )],[refute_0_3,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ big_q(skolemFOFtoCNF_Y_1)
| big_s(skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_0_10:[bind(X_4,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_0_12,plain,
big_s(skolemFOFtoCNF_Y_1),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_Y_1) )],[refute_0_0,refute_0_11]) ).
cnf(refute_0_13,plain,
~ big_s(skolemFOFtoCNF_Y_1),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( big_s(skolemFOFtoCNF_Y_1) )],[refute_0_12,refute_0_13]) ).
fof(negate_1_0,plain,
~ ( ! [Y] :
( big_q(Y)
=> big_s(Y) )
=> ! [X] :
( big_p(X)
=> big_r(X) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
( ? [X] :
( ~ big_r(X)
& big_p(X) )
& ! [Y] :
( ~ big_q(Y)
| big_s(Y) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
? [X] :
( ~ big_r(X)
& big_p(X) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
( ~ big_r(skolemFOFtoCNF_X_1)
& big_p(skolemFOFtoCNF_X_1) ),
inference(skolemize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
big_p(skolemFOFtoCNF_X_1),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [Y] :
( ~ big_q(Y)
| big_s(Y) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_5,plain,
! [Y] :
( ~ big_q(Y)
| big_s(Y) ),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
( ? [X] : big_p(X)
<=> ? [Y] : big_q(Y) ),
inference(canonicalize,[],[pel26_1]) ).
fof(normalize_1_7,plain,
! [X,Y] :
( ( ~ big_p(X)
| big_q(skolemFOFtoCNF_Y) )
& ( ~ big_q(Y)
| big_p(skolemFOFtoCNF_X) ) ),
inference(clausify,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [X] :
( ~ big_p(X)
| big_q(skolemFOFtoCNF_Y) ),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [X,Y] :
( ~ big_p(X)
| ~ big_q(Y)
| ( ~ big_r(X)
<=> ~ big_s(Y) ) ),
inference(canonicalize,[],[pel26_2]) ).
fof(normalize_1_10,plain,
! [X,Y] :
( ~ big_p(X)
| ~ big_q(Y)
| ( ~ big_r(X)
<=> ~ big_s(Y) ) ),
inference(specialize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [X,Y] :
( ( ~ big_p(X)
| ~ big_q(Y)
| ~ big_r(X)
| big_s(Y) )
& ( ~ big_p(X)
| ~ big_q(Y)
| ~ big_s(Y)
| big_r(X) ) ),
inference(clausify,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [X,Y] :
( ~ big_p(X)
| ~ big_q(Y)
| ~ big_s(Y)
| big_r(X) ),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
~ big_r(skolemFOFtoCNF_X_1),
inference(conjunct,[],[normalize_1_2]) ).
cnf(refute_1_0,plain,
big_p(skolemFOFtoCNF_X_1),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( ~ big_q(Y)
| big_s(Y) ),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_2,plain,
( ~ big_q(skolemFOFtoCNF_Y)
| big_s(skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_1_1:[bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_1_3,plain,
( ~ big_p(X)
| big_q(skolemFOFtoCNF_Y) ),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_4,plain,
( ~ big_p(skolemFOFtoCNF_X_1)
| big_q(skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_1_3:[bind(X,$fot(skolemFOFtoCNF_X_1))]]) ).
cnf(refute_1_5,plain,
big_q(skolemFOFtoCNF_Y),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X_1) )],[refute_1_0,refute_1_4]) ).
cnf(refute_1_6,plain,
big_s(skolemFOFtoCNF_Y),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_Y) )],[refute_1_5,refute_1_2]) ).
cnf(refute_1_7,plain,
( ~ big_p(X)
| ~ big_q(Y)
| ~ big_s(Y)
| big_r(X) ),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_8,plain,
( ~ big_p(X_9)
| ~ big_q(skolemFOFtoCNF_Y)
| ~ big_s(skolemFOFtoCNF_Y)
| big_r(X_9) ),
inference(subst,[],[refute_1_7:[bind(X,$fot(X_9)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_1_9,plain,
( ~ big_p(X_9)
| ~ big_q(skolemFOFtoCNF_Y)
| big_r(X_9) ),
inference(resolve,[$cnf( big_s(skolemFOFtoCNF_Y) )],[refute_1_6,refute_1_8]) ).
cnf(refute_1_10,plain,
( ~ big_p(X_9)
| big_r(X_9) ),
inference(resolve,[$cnf( big_q(skolemFOFtoCNF_Y) )],[refute_1_5,refute_1_9]) ).
cnf(refute_1_11,plain,
( ~ big_p(skolemFOFtoCNF_X_1)
| big_r(skolemFOFtoCNF_X_1) ),
inference(subst,[],[refute_1_10:[bind(X_9,$fot(skolemFOFtoCNF_X_1))]]) ).
cnf(refute_1_12,plain,
big_r(skolemFOFtoCNF_X_1),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X_1) )],[refute_1_0,refute_1_11]) ).
cnf(refute_1_13,plain,
~ big_r(skolemFOFtoCNF_X_1),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_14,plain,
$false,
inference(resolve,[$cnf( big_r(skolemFOFtoCNF_X_1) )],[refute_1_12,refute_1_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN056+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n024.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 : Mon Jul 11 22:06:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35
%------------------------------------------------------------------------------