%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU255+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 02:51:31 PM UTC 2026
% Result : Theorem 5.39s 1.15s
% Output : Proof 5.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 6 unt; 0 def)
% Number of atoms : 113 ( 13 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 119 ( 43 ~; 50 |; 16 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 60 ( 5 sgn 28 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> ! [B,C] :
( ( in(ordered_pair(C,B),A)
& in(ordered_pair(B,C),A) )
=> B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_wellord1) ).
fof(f19_nnf,plain,
! [A] :
( ( ( ? [B,C] :
( B != C
& in(ordered_pair(C,B),A)
& in(ordered_pair(B,C),A) )
| antisymmetric(A) )
& ( ! [B,C] :
( B = C
| ~ in(ordered_pair(C,B),A)
| ~ in(ordered_pair(B,C),A) )
| ~ antisymmetric(A) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,B,C] :
( ( ( ( sk1(A) != sk2(A)
& in(ordered_pair(sk2(A),sk1(A)),A)
& in(ordered_pair(sk1(A),sk2(A)),A) )
| antisymmetric(A) )
& ( B = C
| ~ in(ordered_pair(C,B),A)
| ~ in(ordered_pair(B,C),A)
| ~ antisymmetric(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2])],[f19_nnf]) ).
cnf(c22,plain,
( in(ordered_pair(sk1(X0),sk2(X0)),X0)
| antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
fof(f10,axiom,
! [A,B] :
( relation(A)
=> relation(relation_restriction(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f10_nnf,plain,
! [A,B] :
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A,B] :
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c12,plain,
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f27,conjecture,
! [A,B] :
( relation(B)
=> ( antisymmetric(B)
=> antisymmetric(relation_restriction(B,A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_wellord1) ).
fof(f27_neg,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ( antisymmetric(B)
=> antisymmetric(relation_restriction(B,A)) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f27_nnf,plain,
? [A,B] :
( ~ antisymmetric(relation_restriction(B,A))
& antisymmetric(B)
& relation(B) ),
inference(nnf_transformation,[status(thm)],[f27_neg]) ).
fof(f27_sk,plain,
( ~ antisymmetric(relation_restriction(sk9,sk8))
& antisymmetric(sk9)
& relation(sk9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9])],[f27_nnf]) ).
cnf(c39,plain,
relation(sk9),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p63,plain,
relation(relation_restriction(sk9,X0)),
inference(resolution,[status(thm)],[c12,c39]) ).
cnf(p102,plain,
( in(ordered_pair(sk1(relation_restriction(sk9,X0)),sk2(relation_restriction(sk9,X0))),relation_restriction(sk9,X0))
| antisymmetric(relation_restriction(sk9,X0)) ),
inference(resolution,[status(thm)],[c22,p63]) ).
fof(f25,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f25_nnf,plain,
! [A,B,C] :
( ( ( ~ in(A,cartesian_product2(B,B))
| ~ in(A,C)
| in(A,relation_restriction(C,B)) )
& ( ( in(A,cartesian_product2(B,B))
& in(A,C) )
| ~ in(A,relation_restriction(C,B)) ) )
| ~ relation(C) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [C,A,B] :
( ( ( ~ in(A,cartesian_product2(B,B))
| ~ in(A,C)
| in(A,relation_restriction(C,B)) )
& ( ( in(A,cartesian_product2(B,B))
& in(A,C) )
| ~ in(A,relation_restriction(C,B)) ) )
| ~ relation(C) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c35,plain,
( in(X0,X2)
| ~ in(X0,relation_restriction(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p144,plain,
( in(X0,sk9)
| ~ in(X0,relation_restriction(sk9,X1)) ),
inference(resolution,[status(thm)],[c35,c39]) ).
cnf(p181,plain,
( in(ordered_pair(sk1(relation_restriction(sk9,X0)),sk2(relation_restriction(sk9,X0))),sk9)
| antisymmetric(relation_restriction(sk9,X0)) ),
inference(resolution,[status(thm)],[p102,p144]) ).
cnf(c21,plain,
( X1 = X2
| ~ in(ordered_pair(X2,X1),X0)
| ~ in(ordered_pair(X1,X2),X0)
| ~ antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p81,plain,
( X0 = X1
| ~ in(ordered_pair(X1,X0),sk9)
| ~ in(ordered_pair(X0,X1),sk9)
| ~ antisymmetric(sk9) ),
inference(resolution,[status(thm)],[c21,c39]) ).
cnf(c40,plain,
antisymmetric(sk9),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p178,plain,
( X0 = X1
| ~ in(ordered_pair(X1,X0),sk9)
| ~ in(ordered_pair(X0,X1),sk9) ),
inference(resolution,[status(thm)],[p81,c40]) ).
cnf(p187,plain,
( sk1(relation_restriction(sk9,X0)) = sk2(relation_restriction(sk9,X0))
| ~ in(ordered_pair(sk2(relation_restriction(sk9,X0)),sk1(relation_restriction(sk9,X0))),sk9)
| antisymmetric(relation_restriction(sk9,X0)) ),
inference(resolution,[status(thm)],[p181,p178]) ).
cnf(c23,plain,
( in(ordered_pair(sk2(X0),sk1(X0)),X0)
| antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p112,plain,
( in(ordered_pair(sk2(relation_restriction(sk9,X0)),sk1(relation_restriction(sk9,X0))),relation_restriction(sk9,X0))
| antisymmetric(relation_restriction(sk9,X0)) ),
inference(resolution,[status(thm)],[c23,p63]) ).
cnf(p191,plain,
( in(ordered_pair(sk2(relation_restriction(sk9,X0)),sk1(relation_restriction(sk9,X0))),sk9)
| antisymmetric(relation_restriction(sk9,X0)) ),
inference(resolution,[status(thm)],[p112,p144]) ).
cnf(p327,plain,
( antisymmetric(relation_restriction(sk9,X0))
| sk1(relation_restriction(sk9,X0)) = sk2(relation_restriction(sk9,X0))
| antisymmetric(relation_restriction(sk9,X0)) ),
inference(resolution,[status(thm)],[p187,p191]) ).
cnf(p328,plain,
( sk1(relation_restriction(sk9,X0)) = sk2(relation_restriction(sk9,X0))
| antisymmetric(relation_restriction(sk9,X0)) ),
inference(factoring,[status(thm)],[p327]) ).
cnf(c24,plain,
( sk1(X0) != sk2(X0)
| antisymmetric(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p135,plain,
( sk1(relation_restriction(sk9,X0)) != sk2(relation_restriction(sk9,X0))
| antisymmetric(relation_restriction(sk9,X0)) ),
inference(resolution,[status(thm)],[c24,p63]) ).
cnf(p332,plain,
( antisymmetric(relation_restriction(sk9,X0))
| antisymmetric(relation_restriction(sk9,X0)) ),
inference(resolution,[status(thm)],[p328,p135]) ).
cnf(p333,plain,
antisymmetric(relation_restriction(sk9,X0)),
inference(factoring,[status(thm)],[p332]) ).
cnf(c41,plain,
~ antisymmetric(relation_restriction(sk9,sk8)),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p334,plain,
$false,
inference(resolution,[status(thm)],[p333,c41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU255+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.41 % Computer : n018.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Thu Sep 24 13:27:34 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.39/1.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.39/1.15 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------