TSTP Solution File: SEU217+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU217+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 : Tue Jul 19 12:39:24 EDT 2022
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 14 unt; 0 def)
% Number of atoms : 91 ( 37 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 107 ( 48 ~; 40 |; 11 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 45 ( 2 sgn 27 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k6_relat_1,axiom,
! [A] : relation(identity_relation(A)) ).
fof(fc2_funct_1,axiom,
! [A] :
( relation(identity_relation(A))
& function(identity_relation(A)) ) ).
fof(t35_funct_1,conjecture,
! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ) ).
fof(t34_funct_1,axiom,
! [A,B] :
( ( relation(B)
& function(B) )
=> ( B = identity_relation(A)
<=> ( relation_dom(B) = A
& ! [C] :
( in(C,A)
=> apply(B,C) = C ) ) ) ) ).
fof(subgoal_0,plain,
! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
inference(strip,[],[t35_funct_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B] :
( apply(identity_relation(A),B) != B
& in(B,A) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( apply(identity_relation(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B_3) != skolemFOFtoCNF_B_3
& in(skolemFOFtoCNF_B_3,skolemFOFtoCNF_A_6) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
in(skolemFOFtoCNF_B_3,skolemFOFtoCNF_A_6),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ function(B)
| ~ relation(B)
| ( B != identity_relation(A)
<=> ( relation_dom(B) != A
| ? [C] :
( apply(B,C) != C
& in(C,A) ) ) ) ),
inference(canonicalize,[],[t34_funct_1]) ).
fof(normalize_0_4,plain,
! [A,B] :
( ~ function(B)
| ~ relation(B)
| ( B != identity_relation(A)
<=> ( relation_dom(B) != A
| ? [C] :
( apply(B,C) != C
& in(C,A) ) ) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C] :
( ( B != identity_relation(A)
| ~ function(B)
| ~ relation(B)
| relation_dom(B) = A )
& ( B != identity_relation(A)
| ~ function(B)
| ~ in(C,A)
| ~ relation(B)
| apply(B,C) = C )
& ( apply(B,skolemFOFtoCNF_C(A,B)) != skolemFOFtoCNF_C(A,B)
| relation_dom(B) != A
| ~ function(B)
| ~ relation(B)
| B = identity_relation(A) )
& ( relation_dom(B) != A
| ~ function(B)
| ~ relation(B)
| B = identity_relation(A)
| in(skolemFOFtoCNF_C(A,B),A) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C] :
( B != identity_relation(A)
| ~ function(B)
| ~ in(C,A)
| ~ relation(B)
| apply(B,C) = C ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( ! [A] : function(identity_relation(A))
& ! [A] : relation(identity_relation(A)) ),
inference(canonicalize,[],[fc2_funct_1]) ).
fof(normalize_0_8,plain,
! [A] : relation(identity_relation(A)),
inference(canonicalize,[],[dt_k6_relat_1]) ).
fof(normalize_0_9,plain,
! [A] : relation(identity_relation(A)),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A] : function(identity_relation(A)),
inference(simplify,[],[normalize_0_7,normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A] : function(identity_relation(A)),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
apply(identity_relation(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B_3) != skolemFOFtoCNF_B_3,
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
in(skolemFOFtoCNF_B_3,skolemFOFtoCNF_A_6),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( B != identity_relation(A)
| ~ function(B)
| ~ in(C,A)
| ~ relation(B)
| apply(B,C) = C ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( identity_relation(A) != identity_relation(A)
| ~ function(identity_relation(A))
| ~ in(C,A)
| ~ relation(identity_relation(A))
| apply(identity_relation(A),C) = C ),
inference(subst,[],[refute_0_1:[bind(B,$fot(identity_relation(A)))]]) ).
cnf(refute_0_3,plain,
identity_relation(A) = identity_relation(A),
introduced(tautology,[refl,[$fot(identity_relation(A))]]) ).
cnf(refute_0_4,plain,
( ~ function(identity_relation(A))
| ~ in(C,A)
| ~ relation(identity_relation(A))
| apply(identity_relation(A),C) = C ),
inference(resolve,[$cnf( $equal(identity_relation(A),identity_relation(A)) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
function(identity_relation(A)),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_6,plain,
( ~ in(C,A)
| ~ relation(identity_relation(A))
| apply(identity_relation(A),C) = C ),
inference(resolve,[$cnf( function(identity_relation(A)) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
relation(identity_relation(A)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
( ~ in(C,A)
| apply(identity_relation(A),C) = C ),
inference(resolve,[$cnf( relation(identity_relation(A)) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
( ~ in(skolemFOFtoCNF_B_3,skolemFOFtoCNF_A_6)
| apply(identity_relation(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B_3) = skolemFOFtoCNF_B_3 ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_A_6)),bind(C,$fot(skolemFOFtoCNF_B_3))]]) ).
cnf(refute_0_10,plain,
apply(identity_relation(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B_3) = skolemFOFtoCNF_B_3,
inference(resolve,[$cnf( in(skolemFOFtoCNF_B_3,skolemFOFtoCNF_A_6) )],[refute_0_0,refute_0_9]) ).
cnf(refute_0_11,plain,
apply(identity_relation(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B_3) != skolemFOFtoCNF_B_3,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_12,plain,
$false,
inference(resolve,[$cnf( $equal(apply(identity_relation(skolemFOFtoCNF_A_6),skolemFOFtoCNF_B_3),skolemFOFtoCNF_B_3) )],[refute_0_10,refute_0_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU217+3 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n013.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 : Sun Jun 19 20:39:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.37
%------------------------------------------------------------------------------