%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN070+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 08:59:16 EDT 2022
% Result : Theorem 0.14s 0.36s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 50 ( 14 unt; 0 def)
% Number of atoms : 145 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 158 ( 63 ~; 67 |; 20 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 66 ( 15 sgn 34 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel46_1,axiom,
! [X,Y] :
( ( big_f(X)
& ( ( big_f(Y)
& big_h(Y,X) )
=> big_g(Y) ) )
=> big_g(X) ) ).
fof(pel46_2,axiom,
( ? [X] :
( big_f(X)
& ~ big_g(X) )
=> ? [X1] :
( big_f(X1)
& ~ big_g(X1)
& ! [Y] :
( ( big_f(Y)
& ~ big_g(Y) )
=> big_j(X1,Y) ) ) ) ).
fof(pel46_3,axiom,
! [X,Y] :
( ( big_f(X)
& big_f(Y)
& big_h(X,Y) )
=> ~ big_j(Y,X) ) ).
fof(pel46,conjecture,
! [X] :
( big_f(X)
=> big_g(X) ) ).
fof(subgoal_0,plain,
! [X] :
( big_f(X)
=> big_g(X) ),
inference(strip,[],[pel46]) ).
fof(negate_0_0,plain,
~ ! [X] :
( big_f(X)
=> big_g(X) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X] :
( ~ big_g(X)
& big_f(X) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ big_g(skolemFOFtoCNF_X)
& big_f(skolemFOFtoCNF_X) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ big_g(skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X] :
( ~ big_f(X)
| big_g(X)
| ( ! [Y] : ~ big_g(Y)
& ! [Y] : big_f(Y)
& ! [Y] : big_h(Y,X) ) ),
inference(canonicalize,[],[pel46_1]) ).
fof(normalize_0_4,plain,
! [X] :
( ~ big_f(X)
| big_g(X)
| ( ! [Y] : ~ big_g(Y)
& ! [Y] : big_f(Y)
& ! [Y] : big_h(Y,X) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ( ~ big_f(X)
| ~ big_g(Y)
| big_g(X) )
& ( ~ big_f(X)
| big_f(Y)
| big_g(X) )
& ( ~ big_f(X)
| big_g(X)
| big_h(Y,X) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ big_f(X)
| ~ big_g(Y)
| big_g(X) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
big_f(skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ big_f(X)
| big_f(Y)
| big_g(X) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ big_f(X)
| big_g(X)
| big_h(Y,X) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_10,plain,
( ? [X1] :
( ~ big_g(X1)
& big_f(X1)
& ! [Y] :
( ~ big_f(Y)
| big_g(Y)
| big_j(X1,Y) ) )
| ! [X] :
( ~ big_f(X)
| big_g(X) ) ),
inference(canonicalize,[],[pel46_2]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ( ~ big_f(X)
| ~ big_g(skolemFOFtoCNF_X1)
| big_g(X) )
& ( ~ big_f(X)
| big_f(skolemFOFtoCNF_X1)
| big_g(X) )
& ( ~ big_f(X)
| ~ big_f(Y)
| big_g(X)
| big_g(Y)
| big_j(skolemFOFtoCNF_X1,Y) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ big_f(X)
| ~ big_f(Y)
| big_g(X)
| big_g(Y)
| big_j(skolemFOFtoCNF_X1,Y) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_h(X,Y)
| ~ big_j(Y,X) ),
inference(canonicalize,[],[pel46_3]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_h(X,Y)
| ~ big_j(Y,X) ),
inference(specialize,[],[normalize_0_13]) ).
cnf(refute_0_0,plain,
~ big_g(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ big_f(X)
| ~ big_g(Y)
| big_g(X) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ big_f(X_5)
| ~ big_g(Y)
| big_g(X_5) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(X_5))]]) ).
cnf(refute_0_3,plain,
big_f(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
( ~ big_f(X)
| big_f(Y)
| big_g(X) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ big_f(skolemFOFtoCNF_X)
| big_f(X_4)
| big_g(skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(X_4))]]) ).
cnf(refute_0_6,plain,
( big_f(X_4)
| big_g(skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
big_f(X_4),
inference(resolve,[$cnf( big_g(skolemFOFtoCNF_X) )],[refute_0_6,refute_0_0]) ).
cnf(refute_0_8,plain,
big_f(X_5),
inference(subst,[],[refute_0_7:[bind(X_4,$fot(X_5))]]) ).
cnf(refute_0_9,plain,
( ~ big_g(Y)
| big_g(X_5) ),
inference(resolve,[$cnf( big_f(X_5) )],[refute_0_8,refute_0_2]) ).
cnf(refute_0_10,plain,
( ~ big_g(skolemFOFtoCNF_X1)
| big_g(X_5) ),
inference(subst,[],[refute_0_9:[bind(Y,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_11,plain,
( ~ big_f(X)
| big_g(X)
| big_h(Y,X) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_12,plain,
big_f(X),
inference(subst,[],[refute_0_7:[bind(X_4,$fot(X))]]) ).
cnf(refute_0_13,plain,
( big_g(X)
| big_h(Y,X) ),
inference(resolve,[$cnf( big_f(X) )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
( big_g(skolemFOFtoCNF_X1)
| big_h(skolemFOFtoCNF_X,skolemFOFtoCNF_X1) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(skolemFOFtoCNF_X1)),bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_15,plain,
( ~ big_f(X)
| ~ big_f(Y)
| big_g(X)
| big_g(Y)
| big_j(skolemFOFtoCNF_X1,Y) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_16,plain,
( ~ big_f(skolemFOFtoCNF_X)
| big_g(skolemFOFtoCNF_X)
| big_j(skolemFOFtoCNF_X1,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_17,plain,
( big_g(skolemFOFtoCNF_X)
| big_j(skolemFOFtoCNF_X1,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X) )],[refute_0_3,refute_0_16]) ).
cnf(refute_0_18,plain,
big_j(skolemFOFtoCNF_X1,skolemFOFtoCNF_X),
inference(resolve,[$cnf( big_g(skolemFOFtoCNF_X) )],[refute_0_17,refute_0_0]) ).
cnf(refute_0_19,plain,
( ~ big_f(X)
| ~ big_f(Y)
| ~ big_h(X,Y)
| ~ big_j(Y,X) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_20,plain,
( ~ big_f(Y)
| ~ big_h(X,Y)
| ~ big_j(Y,X) ),
inference(resolve,[$cnf( big_f(X) )],[refute_0_12,refute_0_19]) ).
cnf(refute_0_21,plain,
big_f(Y),
inference(subst,[],[refute_0_7:[bind(X_4,$fot(Y))]]) ).
cnf(refute_0_22,plain,
( ~ big_h(X,Y)
| ~ big_j(Y,X) ),
inference(resolve,[$cnf( big_f(Y) )],[refute_0_21,refute_0_20]) ).
cnf(refute_0_23,plain,
( ~ big_h(skolemFOFtoCNF_X,skolemFOFtoCNF_X1)
| ~ big_j(skolemFOFtoCNF_X1,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_24,plain,
~ big_h(skolemFOFtoCNF_X,skolemFOFtoCNF_X1),
inference(resolve,[$cnf( big_j(skolemFOFtoCNF_X1,skolemFOFtoCNF_X) )],[refute_0_18,refute_0_23]) ).
cnf(refute_0_25,plain,
big_g(skolemFOFtoCNF_X1),
inference(resolve,[$cnf( big_h(skolemFOFtoCNF_X,skolemFOFtoCNF_X1) )],[refute_0_14,refute_0_24]) ).
cnf(refute_0_26,plain,
big_g(X_5),
inference(resolve,[$cnf( big_g(skolemFOFtoCNF_X1) )],[refute_0_25,refute_0_10]) ).
cnf(refute_0_27,plain,
big_g(skolemFOFtoCNF_X),
inference(subst,[],[refute_0_26:[bind(X_5,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_28,plain,
$false,
inference(resolve,[$cnf( big_g(skolemFOFtoCNF_X) )],[refute_0_27,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN070+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n006.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
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jul 11 20:42:50 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36
% 0.14/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.36
%------------------------------------------------------------------------------