TSTP Solution File: SYN063+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN063+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 08:59:09 EDT 2022
% Result : Theorem 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 43 ( 25 unt; 0 def)
% Number of atoms : 138 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 155 ( 60 ~; 38 |; 32 &)
% ( 1 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 32 ( 2 sgn 25 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel33,conjecture,
( ! [X] :
( ( big_p(a)
& ( big_p(X)
=> big_p(b) ) )
=> big_p(c) )
<=> ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(c) )
& ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ) ) ) ).
fof(subgoal_0,plain,
( ! [X] :
( ( big_p(a)
& ( big_p(X)
=> big_p(b) ) )
=> big_p(c) )
=> ! [X1] :
( ( ~ ~ big_p(a)
& ~ big_p(X1) )
=> big_p(c) ) ),
inference(strip,[],[pel33]) ).
fof(subgoal_1,plain,
( ! [X] :
( ( big_p(a)
& ( big_p(X)
=> big_p(b) ) )
=> big_p(c) )
=> ! [X1] :
( ( ( ~ big_p(a)
| big_p(X1)
| big_p(c) )
& ~ ~ big_p(a)
& ~ ~ big_p(b) )
=> big_p(c) ) ),
inference(strip,[],[pel33]) ).
fof(subgoal_2,plain,
( ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(c) )
& ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ) )
=> ! [X] :
( ( big_p(a)
& ( big_p(X)
=> big_p(b) ) )
=> big_p(c) ) ),
inference(strip,[],[pel33]) ).
fof(negate_0_0,plain,
~ ( ! [X] :
( ( big_p(a)
& ( big_p(X)
=> big_p(b) ) )
=> big_p(c) )
=> ! [X1] :
( ( ~ ~ big_p(a)
& ~ big_p(X1) )
=> big_p(c) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ big_p(c)
& big_p(a)
& ( ~ big_p(a)
| big_p(c)
| ( ~ big_p(b)
& ! [X] : big_p(X) ) )
& ? [X1] : ~ big_p(X1) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
? [X1] : ~ big_p(X1),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ big_p(skolemFOFtoCNF_X1),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ~ big_p(a)
| big_p(c)
| ( ~ big_p(b)
& ! [X] : big_p(X) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_4,plain,
big_p(a),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_5,plain,
~ big_p(c),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_6,plain,
( ~ big_p(b)
& ! [X] : big_p(X) ),
inference(simplify,[],[normalize_0_3,normalize_0_4,normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X] : big_p(X),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X] : big_p(X),
inference(specialize,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
~ big_p(skolemFOFtoCNF_X1),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
big_p(X),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_2,plain,
big_p(skolemFOFtoCNF_X1),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_3,plain,
$false,
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X1) )],[refute_0_2,refute_0_0]) ).
fof(negate_1_0,plain,
~ ( ! [X] :
( ( big_p(a)
& ( big_p(X)
=> big_p(b) ) )
=> big_p(c) )
=> ! [X1] :
( ( ( ~ big_p(a)
| big_p(X1)
| big_p(c) )
& ~ ~ big_p(a)
& ~ ~ big_p(b) )
=> big_p(c) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
( ~ big_p(c)
& big_p(a)
& big_p(b)
& ( ~ big_p(a)
| big_p(c)
| ( ~ big_p(b)
& ! [X] : big_p(X) ) )
& ( ~ big_p(a)
| big_p(c)
| ? [X1] : big_p(X1) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ~ big_p(a)
| big_p(c)
| ( ~ big_p(b)
& ! [X] : big_p(X) ) ),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
big_p(a),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_3,plain,
~ big_p(c),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_4,plain,
big_p(b),
inference(conjunct,[],[normalize_1_0]) ).
fof(normalize_1_5,plain,
$false,
inference(simplify,[],[normalize_1_1,normalize_1_2,normalize_1_3,normalize_1_4]) ).
cnf(refute_1_0,plain,
$false,
inference(canonicalize,[],[normalize_1_5]) ).
fof(negate_2_0,plain,
~ ( ! [X1] :
( ( ~ big_p(a)
| big_p(X1)
| big_p(c) )
& ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ) )
=> ! [X] :
( ( big_p(a)
& ( big_p(X)
=> big_p(b) ) )
=> big_p(c) ) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
( ~ big_p(c)
& big_p(a)
& ( big_p(b)
| ? [X] : ~ big_p(X) )
& ( ~ big_p(a)
| ~ big_p(b)
| big_p(c) )
& ( ~ big_p(a)
| big_p(c)
| ! [X1] : big_p(X1) ) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_1,plain,
( big_p(b)
| ? [X] : ~ big_p(X) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
( ~ big_p(skolemFOFtoCNF_X)
| big_p(b) ),
inference(clausify,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
( ~ big_p(a)
| big_p(c)
| ! [X1] : big_p(X1) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_4,plain,
big_p(a),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_5,plain,
~ big_p(c),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_6,plain,
! [X1] : big_p(X1),
inference(simplify,[],[normalize_2_3,normalize_2_4,normalize_2_5]) ).
fof(normalize_2_7,plain,
! [X1] : big_p(X1),
inference(specialize,[],[normalize_2_6]) ).
fof(normalize_2_8,plain,
( ~ big_p(a)
| ~ big_p(b)
| big_p(c) ),
inference(conjunct,[],[normalize_2_0]) ).
fof(normalize_2_9,plain,
~ big_p(b),
inference(simplify,[],[normalize_2_8,normalize_2_4,normalize_2_5]) ).
cnf(refute_2_0,plain,
( ~ big_p(skolemFOFtoCNF_X)
| big_p(b) ),
inference(canonicalize,[],[normalize_2_2]) ).
cnf(refute_2_1,plain,
big_p(X1),
inference(canonicalize,[],[normalize_2_7]) ).
cnf(refute_2_2,plain,
big_p(skolemFOFtoCNF_X),
inference(subst,[],[refute_2_1:[bind(X1,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_2_3,plain,
big_p(b),
inference(resolve,[$cnf( big_p(skolemFOFtoCNF_X) )],[refute_2_2,refute_2_0]) ).
cnf(refute_2_4,plain,
~ big_p(b),
inference(canonicalize,[],[normalize_2_9]) ).
cnf(refute_2_5,plain,
$false,
inference(resolve,[$cnf( big_p(b) )],[refute_2_3,refute_2_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN063+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n015.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 : Tue Jul 12 03:26:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34
% 0.12/0.34 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35
%------------------------------------------------------------------------------