%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU239+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 : n016.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 02:51:27 PM UTC 2026
% Result : Theorem 4.71s 1.08s
% Output : Proof 4.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 7 unt; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 113 ( 42 ~; 46 |; 14 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 18 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> is_reflexive_in(A,relation_field(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_relat_2) ).
fof(f8_nnf,plain,
! [A] :
( ( ( ~ is_reflexive_in(A,relation_field(A))
| reflexive(A) )
& ( is_reflexive_in(A,relation_field(A))
| ~ reflexive(A) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A] :
( ( ( ~ is_reflexive_in(A,relation_field(A))
| reflexive(A) )
& ( is_reflexive_in(A,relation_field(A))
| ~ reflexive(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c13,plain,
( ~ is_reflexive_in(X0,relation_field(X0))
| reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f24,conjecture,
! [A] :
( relation(A)
=> ( reflexive(A)
<=> ! [B] :
( in(B,relation_field(A))
=> in(ordered_pair(B,B),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_wellord1) ).
fof(f24_neg,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( reflexive(A)
<=> ! [B] :
( in(B,relation_field(A))
=> in(ordered_pair(B,B),A) ) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f24_nnf,plain,
? [A] :
( ( ( ! [B] :
( in(ordered_pair(B,B),A)
| ~ in(B,relation_field(A)) )
& ~ reflexive(A) )
| ( ? [B] :
( ~ in(ordered_pair(B,B),A)
& in(B,relation_field(A)) )
& reflexive(A) ) )
& relation(A) ),
inference(nnf_transformation,[status(thm)],[f24_neg]) ).
fof(f24_sk,plain,
! [B] :
( ( ( ( in(ordered_pair(B,B),sk2)
| ~ in(B,relation_field(sk2)) )
& ~ reflexive(sk2) )
| ( ~ in(ordered_pair(sk3,sk3),sk2)
& in(sk3,relation_field(sk2))
& reflexive(sk2) ) )
& relation(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f24_nnf]) ).
cnf(c29,plain,
relation(sk2),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p103,plain,
( ~ is_reflexive_in(sk2,relation_field(sk2))
| reflexive(sk2) ),
inference(resolution,[status(thm)],[c13,c29]) ).
fof(f5,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_reflexive_in(A,B)
<=> ! [C] :
( in(C,B)
=> in(ordered_pair(C,C),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_2) ).
fof(f5_nnf,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ~ in(ordered_pair(C,C),A)
& in(C,B) )
| is_reflexive_in(A,B) )
& ( ! [C] :
( in(ordered_pair(C,C),A)
| ~ in(C,B) )
| ~ is_reflexive_in(A,B) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C] :
( ( ( ( ~ in(ordered_pair(sk0(A,B),sk0(A,B)),A)
& in(sk0(A,B),B) )
| is_reflexive_in(A,B) )
& ( in(ordered_pair(C,C),A)
| ~ in(C,B)
| ~ is_reflexive_in(A,B) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f5_nnf]) ).
cnf(c9,plain,
( ~ in(ordered_pair(sk0(X0,X1),sk0(X0,X1)),X0)
| is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p72,plain,
( ~ in(ordered_pair(sk0(sk2,X0),sk0(sk2,X0)),sk2)
| is_reflexive_in(sk2,X0) ),
inference(resolution,[status(thm)],[c9,c29]) ).
cnf(c8,plain,
( in(sk0(X0,X1),X1)
| is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p64,plain,
( in(sk0(sk2,X0),X0)
| is_reflexive_in(sk2,X0) ),
inference(resolution,[status(thm)],[c8,c29]) ).
cnf(c31,plain,
( in(ordered_pair(X1,X1),sk2)
| ~ in(X1,relation_field(sk2))
| reflexive(sk2) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p70,plain,
( in(ordered_pair(sk0(sk2,relation_field(sk2)),sk0(sk2,relation_field(sk2))),sk2)
| reflexive(sk2)
| is_reflexive_in(sk2,relation_field(sk2)) ),
inference(resolution,[status(thm)],[p64,c31]) ).
cnf(p76,plain,
( reflexive(sk2)
| is_reflexive_in(sk2,relation_field(sk2))
| is_reflexive_in(sk2,relation_field(sk2)) ),
inference(resolution,[status(thm)],[p72,p70]) ).
cnf(p77,plain,
( reflexive(sk2)
| is_reflexive_in(sk2,relation_field(sk2)) ),
inference(factoring,[status(thm)],[p76]) ).
cnf(p108,plain,
( reflexive(sk2)
| reflexive(sk2) ),
inference(resolution,[status(thm)],[p103,p77]) ).
cnf(p110,plain,
reflexive(sk2),
inference(factoring,[status(thm)],[p108]) ).
cnf(c12,plain,
( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p97,plain,
( is_reflexive_in(sk2,relation_field(sk2))
| ~ reflexive(sk2) ),
inference(resolution,[status(thm)],[c12,c29]) ).
cnf(p112,plain,
is_reflexive_in(sk2,relation_field(sk2)),
inference(resolution,[status(thm)],[p110,p97]) ).
cnf(c7,plain,
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,X1)
| ~ is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p58,plain,
( in(ordered_pair(X1,X1),sk2)
| ~ in(X1,X0)
| ~ is_reflexive_in(sk2,X0) ),
inference(resolution,[status(thm)],[c7,c29]) ).
cnf(p116,plain,
( in(ordered_pair(X0,X0),sk2)
| ~ in(X0,relation_field(sk2)) ),
inference(resolution,[status(thm)],[p112,p58]) ).
cnf(c32,plain,
( ~ reflexive(sk2)
| in(sk3,relation_field(sk2)) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p111,plain,
in(sk3,relation_field(sk2)),
inference(resolution,[status(thm)],[p110,c32]) ).
cnf(p117,plain,
in(ordered_pair(sk3,sk3),sk2),
inference(resolution,[status(thm)],[p116,p111]) ).
cnf(c34,plain,
( ~ reflexive(sk2)
| ~ in(ordered_pair(sk3,sk3),sk2) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p119,plain,
~ reflexive(sk2),
inference(resolution,[status(thm)],[p117,c34]) ).
cnf(p121,plain,
$false,
inference(resolution,[status(thm)],[p119,p110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU239+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 13:26:44 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.71/1.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.71/1.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------