TSTP Solution File: SYN084+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN084+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 08:59:27 EDT 2022
% Result : Theorem 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 63 ( 21 unt; 0 def)
% Number of atoms : 204 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 224 ( 83 ~; 65 |; 51 &)
% ( 1 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 44 ( 0 sgn 34 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel62,conjecture,
( ! [X] :
( ( big_p(a)
& ( big_p(X)
=> big_p(f(X)) ) )
=> big_p(f(f(X))) )
<=> ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(f(f(X1))) )
& ( ~ big_p(a)
| ~ big_p(f(X1))
| big_p(f(f(X1))) ) ) ) ).
fof(subgoal_0,plain,
( ! [X] :
( ( big_p(a)
& ( big_p(X)
=> big_p(f(X)) ) )
=> big_p(f(f(X))) )
=> ! [X1] :
( ( ~ ~ big_p(a)
& ~ big_p(X1) )
=> big_p(f(f(X1))) ) ),
inference(strip,[],[pel62]) ).
fof(subgoal_1,plain,
( ! [X] :
( ( big_p(a)
& ( big_p(X)
=> big_p(f(X)) ) )
=> big_p(f(f(X))) )
=> ! [X1] :
( ( ( ~ big_p(a)
| big_p(X1)
| big_p(f(f(X1))) )
& ~ ~ big_p(a)
& ~ ~ big_p(f(X1)) )
=> big_p(f(f(X1))) ) ),
inference(strip,[],[pel62]) ).
fof(subgoal_2,plain,
( ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(f(f(X1))) )
& ( ~ big_p(a)
| ~ big_p(f(X1))
| big_p(f(f(X1))) ) )
=> ! [X] :
( ( big_p(a)
& ( big_p(X)
=> big_p(f(X)) ) )
=> big_p(f(f(X))) ) ),
inference(strip,[],[pel62]) ).
fof(negate_0_0,plain,
~ ( ! [X] :
( ( big_p(a)
& ( big_p(X)
=> big_p(f(X)) ) )
=> big_p(f(f(X))) )
=> ! [X1] :
( ( ~ ~ big_p(a)
& ~ big_p(X1) )
=> big_p(f(f(X1))) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ? [X1] :
( ~ big_p(X1)
& ~ big_p(f(f(X1)))
& big_p(a) )
& ! [X] :
( ~ big_p(a)
| big_p(f(f(X)))
| ( ~ big_p(f(X))
& big_p(X) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
? [X1] :
( ~ big_p(X1)
& ~ big_p(f(f(X1)))
& big_p(a) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( ~ big_p(f(f(skolemFOFtoCNF_X1)))
& ~ big_p(skolemFOFtoCNF_X1)
& big_p(a) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ big_p(f(f(skolemFOFtoCNF_X1))),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] :
( ~ big_p(a)
| big_p(f(f(X)))
| ( ~ big_p(f(X))
& big_p(X) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_5,plain,
big_p(a),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_6,plain,
! [X] :
( big_p(f(f(X)))
| ( ~ big_p(f(X))
& big_p(X) ) ),
inference(simplify,[],[normalize_0_4,normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X] :
( big_p(f(f(X)))
| ( ~ big_p(f(X))
& big_p(X) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X] :
( ( ~ big_p(f(X))
| big_p(f(f(X))) )
& ( big_p(X)
| big_p(f(f(X))) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X] :
( big_p(X)
| big_p(f(f(X))) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
~ big_p(skolemFOFtoCNF_X1),
inference(conjunct,[],[normalize_0_2]) ).
cnf(refute_0_0,plain,
~ big_p(f(f(skolemFOFtoCNF_X1))),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( big_p(X)
| big_p(f(f(X))) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_2,plain,
( big_p(f(f(skolemFOFtoCNF_X1)))
| big_p(skolemFOFtoCNF_X1) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_3,plain,
big_p(skolemFOFtoCNF_X1),
inference(resolve,[$cnf( big_p(f(f(skolemFOFtoCNF_X1))) )],[refute_0_2,refute_0_0]) ).
cnf(refute_0_4,plain,
~ big_p(skolemFOFtoCNF_X1),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_5,plain,
$false,
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X1) )],[refute_0_3,refute_0_4]) ).
fof(negate_1_0,plain,
~ ( ! [X] :
( ( big_p(a)
& ( big_p(X)
=> big_p(f(X)) ) )
=> big_p(f(f(X))) )
=> ! [X1] :
( ( ( ~ big_p(a)
| big_p(X1)
| big_p(f(f(X1))) )
& ~ ~ big_p(a)
& ~ ~ big_p(f(X1)) )
=> big_p(f(f(X1))) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
( ? [X1] :
( ~ big_p(f(f(X1)))
& big_p(a)
& big_p(f(X1))
& ( ~ big_p(a)
| big_p(X1)
| big_p(f(f(X1))) ) )
& ! [X] :
( ~ big_p(a)
| big_p(f(f(X)))
| ( ~ big_p(f(X))
& big_p(X) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
? [X1] :
( ~ big_p(f(f(X1)))
& big_p(a)
& big_p(f(X1))
& ( ~ big_p(a)
| big_p(X1)
| big_p(f(f(X1))) ) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
( ~ big_p(f(f(skolemFOFtoCNF_X1_1)))
& big_p(a)
& big_p(f(skolemFOFtoCNF_X1_1))
& ( ~ big_p(a)
| big_p(f(f(skolemFOFtoCNF_X1_1)))
| big_p(skolemFOFtoCNF_X1_1) ) ),
inference(skolemize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
big_p(f(skolemFOFtoCNF_X1_1)),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [X] :
( ~ big_p(a)
| big_p(f(f(X)))
| ( ~ big_p(f(X))
& big_p(X) ) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_5,plain,
big_p(a),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_6,plain,
! [X] :
( big_p(f(f(X)))
| ( ~ big_p(f(X))
& big_p(X) ) ),
inference(simplify,[],[normalize_1_4,normalize_1_5]) ).
fof(normalize_1_7,plain,
! [X] :
( big_p(f(f(X)))
| ( ~ big_p(f(X))
& big_p(X) ) ),
inference(specialize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [X] :
( ( ~ big_p(f(X))
| big_p(f(f(X))) )
& ( big_p(X)
| big_p(f(f(X))) ) ),
inference(clausify,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [X] :
( ~ big_p(f(X))
| big_p(f(f(X))) ),
inference(conjunct,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
~ big_p(f(f(skolemFOFtoCNF_X1_1))),
inference(conjunct,[],[normalize_1_2]) ).
cnf(refute_1_0,plain,
big_p(f(skolemFOFtoCNF_X1_1)),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( ~ big_p(f(X))
| big_p(f(f(X))) ),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_2,plain,
( ~ big_p(f(skolemFOFtoCNF_X1_1))
| big_p(f(f(skolemFOFtoCNF_X1_1))) ),
inference(subst,[],[refute_1_1:[bind(X,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_1_3,plain,
big_p(f(f(skolemFOFtoCNF_X1_1))),
inference(resolve,[$cnf( big_p(f(skolemFOFtoCNF_X1_1)) )],[refute_1_0,refute_1_2]) ).
cnf(refute_1_4,plain,
~ big_p(f(f(skolemFOFtoCNF_X1_1))),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_5,plain,
$false,
inference(resolve,[$cnf( big_p(f(f(skolemFOFtoCNF_X1_1))) )],[refute_1_3,refute_1_4]) ).
fof(negate_2_0,plain,
~ ( ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(f(f(X1))) )
& ( ~ big_p(a)
| ~ big_p(f(X1))
| big_p(f(f(X1))) ) )
=> ! [X] :
( ( big_p(a)
& ( big_p(X)
=> big_p(f(X)) ) )
=> big_p(f(f(X))) ) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
( ? [X] :
( ~ big_p(f(f(X)))
& big_p(a)
& ( ~ big_p(X)
| big_p(f(X)) ) )
& ! [X1] :
( ~ big_p(a)
| ~ big_p(f(X1))
| big_p(f(f(X1))) )
& ! [X1] :
( ~ big_p(a)
| big_p(X1)
| big_p(f(f(X1))) ) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
? [X] :
( ~ big_p(f(f(X)))
& big_p(a)
& ( ~ big_p(X)
| big_p(f(X)) ) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
( ~ big_p(f(f(skolemFOFtoCNF_X)))
& big_p(a)
& ( ~ big_p(skolemFOFtoCNF_X)
| big_p(f(skolemFOFtoCNF_X)) ) ),
inference(skolemize,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
( ~ big_p(skolemFOFtoCNF_X)
| big_p(f(skolemFOFtoCNF_X)) ),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_4,plain,
~ big_p(f(f(skolemFOFtoCNF_X))),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_5,plain,
! [X1] :
( ~ big_p(a)
| big_p(X1)
| big_p(f(f(X1))) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_6,plain,
big_p(a),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_7,plain,
! [X1] :
( big_p(X1)
| big_p(f(f(X1))) ),
inference(simplify,[],[normalize_2_5,normalize_2_6]) ).
fof(normalize_2_8,plain,
! [X1] :
( big_p(X1)
| big_p(f(f(X1))) ),
inference(specialize,[],[normalize_2_7]) ).
fof(normalize_2_9,plain,
! [X1] :
( ~ big_p(a)
| ~ big_p(f(X1))
| big_p(f(f(X1))) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_10,plain,
! [X1] :
( ~ big_p(f(X1))
| big_p(f(f(X1))) ),
inference(simplify,[],[normalize_2_9,normalize_2_6]) ).
fof(normalize_2_11,plain,
! [X1] :
( ~ big_p(f(X1))
| big_p(f(f(X1))) ),
inference(specialize,[],[normalize_2_10]) ).
cnf(refute_2_0,plain,
( ~ big_p(skolemFOFtoCNF_X)
| big_p(f(skolemFOFtoCNF_X)) ),
inference(canonicalize,[],[normalize_2_3]) ).
cnf(refute_2_1,plain,
~ big_p(f(f(skolemFOFtoCNF_X))),
inference(canonicalize,[],[normalize_2_4]) ).
cnf(refute_2_2,plain,
( big_p(X1)
| big_p(f(f(X1))) ),
inference(canonicalize,[],[normalize_2_8]) ).
cnf(refute_2_3,plain,
( big_p(f(f(skolemFOFtoCNF_X)))
| big_p(skolemFOFtoCNF_X) ),
inference(subst,[],[refute_2_2:[bind(X1,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_2_4,plain,
big_p(skolemFOFtoCNF_X),
inference(resolve,[$cnf( big_p(f(f(skolemFOFtoCNF_X))) )],[refute_2_3,refute_2_1]) ).
cnf(refute_2_5,plain,
big_p(f(skolemFOFtoCNF_X)),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X) )],[refute_2_4,refute_2_0]) ).
cnf(refute_2_6,plain,
( ~ big_p(f(X1))
| big_p(f(f(X1))) ),
inference(canonicalize,[],[normalize_2_11]) ).
cnf(refute_2_7,plain,
( ~ big_p(f(skolemFOFtoCNF_X))
| big_p(f(f(skolemFOFtoCNF_X))) ),
inference(subst,[],[refute_2_6:[bind(X1,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_2_8,plain,
big_p(f(f(skolemFOFtoCNF_X))),
inference(resolve,[$cnf( big_p(f(skolemFOFtoCNF_X)) )],[refute_2_5,refute_2_7]) ).
cnf(refute_2_9,plain,
$false,
inference(resolve,[$cnf( big_p(f(f(skolemFOFtoCNF_X))) )],[refute_2_8,refute_2_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN084+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n022.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 12:53:55 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
%------------------------------------------------------------------------------