%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU217+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:51:22 PM UTC 2026
% Result : Theorem 24.80s 3.86s
% Output : Proof 24.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 10 unt; 0 def)
% Number of atoms : 64 ( 27 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 67 ( 27 ~; 22 |; 13 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 2 sgn 19 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f30,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( B = identity_relation(A)
<=> ( ! [C] :
( in(C,A)
=> apply(B,C) = C )
& relation_dom(B) = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f30_nnf,plain,
! [A,B] :
( ( ( ? [C] :
( apply(B,C) != C
& in(C,A) )
| relation_dom(B) != A
| B = identity_relation(A) )
& ( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [B,A,C] :
( ( ( ( apply(B,sk11(A,B)) != sk11(A,B)
& in(sk11(A,B),A) )
| relation_dom(B) != A
| B = identity_relation(A) )
& ( ( ( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f30_nnf]) ).
cnf(c44,plain,
( apply(X1,X2) = X2
| ~ in(X2,X0)
| X1 != identity_relation(X0)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(p123,plain,
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[status(thm)],[c44]) ).
fof(f17,axiom,
! [A] : relation(identity_relation(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f17_nnf,plain,
! [A] : relation(identity_relation(A)),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [A] : relation(identity_relation(A)),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c22,plain,
relation(identity_relation(X0)),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p175,plain,
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0)
| ~ function(identity_relation(X0)) ),
inference(resolution,[status(thm)],[p123,c22]) ).
fof(f18,axiom,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f18_nnf,plain,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c24,plain,
function(identity_relation(X0)),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p181,plain,
( apply(identity_relation(X1),X0) = X0
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[p175,c24]) ).
fof(f29,conjecture,
! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
fof(f29_neg,negated_conjecture,
~ ! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f29_nnf,plain,
? [A,B] :
( apply(identity_relation(A),B) != B
& in(B,A) ),
inference(nnf_transformation,[status(thm)],[f29_neg]) ).
fof(f29_sk,plain,
( apply(identity_relation(sk9),sk10) != sk10
& in(sk10,sk9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9,sk10])],[f29_nnf]) ).
cnf(c41,plain,
in(sk10,sk9),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p183,plain,
apply(identity_relation(sk9),sk10) = sk10,
inference(resolution,[status(thm)],[p181,c41]) ).
cnf(c42,plain,
apply(identity_relation(sk9),sk10) != sk10,
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p184,plain,
sk10 != sk10,
inference(demodulation,[status(thm)],[p183,c42]) ).
cnf(p190,plain,
$false,
inference(equality_resolution,[status(thm)],[p184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU217+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.58 % Computer : n010.cluster.edu
% 0.09/0.58 % Model : x86_64 x86_64
% 0.09/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.58 % Memory : 8046.5625MB
% 0.09/0.58 % OS : Linux 6.8.0-71-generic
% 0.09/0.58 % CPULimit : 300
% 0.09/0.58 % WCLimit : 300
% 0.09/0.58 % DateTime : Thu Sep 24 13:14:30 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.58 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.80/3.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.80/3.86 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------