%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU209+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 02:51:20 PM UTC 2026
% Result : Theorem 29.18s 4.30s
% Output : Proof 29.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 4 unt; 0 def)
% Number of atoms : 116 ( 14 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 139 ( 51 ~; 51 |; 27 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-4 aty)
% Number of variables : 79 ( 4 sgn 40 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f5_nnf,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
& ~ in(C,B) )
| ( ! [D] : ~ in(ordered_pair(C,D),A)
& in(C,B) ) )
| B = relation_dom(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C,D] :
( ( ( ( in(ordered_pair(sk5(A,B),sk6(A,B)),A)
& ~ in(sk5(A,B),B) )
| ( ~ in(ordered_pair(sk5(A,B),D),A)
& in(sk5(A,B),B) )
| B = relation_dom(A) )
& ( ( ( ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( in(ordered_pair(C,sk4(A,B,C)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6])],[f5_nnf]) ).
cnf(c16,plain,
( ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f31,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_inverse_image(B,A),relation_dom(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t167_relat_1) ).
fof(f31_neg,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_inverse_image(B,A),relation_dom(B)) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f31_nnf,plain,
? [A,B] :
( ~ subset(relation_inverse_image(B,A),relation_dom(B))
& relation(B) ),
inference(nnf_transformation,[status(thm)],[f31_neg]) ).
fof(f31_sk,plain,
( ~ subset(relation_inverse_image(sk15,sk14),relation_dom(sk15))
& relation(sk15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk14,sk15])],[f31_nnf]) ).
cnf(c52,plain,
relation(sk15),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p191,plain,
( ~ in(ordered_pair(X1,X2),sk15)
| in(X1,X0)
| X0 != relation_dom(sk15) ),
inference(resolution,[status(thm)],[c16,c52]) ).
cnf(p197,plain,
( ~ in(ordered_pair(X0,X1),sk15)
| in(X0,relation_dom(sk15)) ),
inference(equality_resolution,[status(thm)],[p191]) ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f4_nnf,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk3(A,B),B)
& in(sk3(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f4_nnf]) ).
cnf(c13,plain,
( in(sk3(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f3,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f3_nnf,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
& ~ in(D,C) )
| ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
& in(D,C) ) )
| C = relation_inverse_image(A,B) )
& ( ! [D] :
( ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| in(D,C) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,C,B,D,E] :
( ( ( ( in(sk2(A,B,C),B)
& in(ordered_pair(sk1(A,B,C),sk2(A,B,C)),A)
& ~ in(sk1(A,B,C),C) )
| ( ( ~ in(E,B)
| ~ in(ordered_pair(sk1(A,B,C),E),A) )
& in(sk1(A,B,C),C) )
| C = relation_inverse_image(A,B) )
& ( ( ( ~ in(E,B)
| ~ in(ordered_pair(D,E),A)
| in(D,C) )
& ( ( in(sk0(A,B,C,D),B)
& in(ordered_pair(D,sk0(A,B,C,D)),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f3_nnf]) ).
cnf(c3,plain,
( in(ordered_pair(X3,sk0(X0,X1,X2,X3)),X0)
| ~ in(X3,X2)
| X2 != relation_inverse_image(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p66,plain,
( in(ordered_pair(X2,sk0(sk15,X1,X0,X2)),sk15)
| ~ in(X2,X0)
| X0 != relation_inverse_image(sk15,X1) ),
inference(resolution,[status(thm)],[c3,c52]) ).
cnf(p69,plain,
( in(ordered_pair(X0,sk0(sk15,X1,relation_inverse_image(sk15,X1),X0)),sk15)
| ~ in(X0,relation_inverse_image(sk15,X1)) ),
inference(equality_resolution,[status(thm)],[p66]) ).
cnf(p160,plain,
( in(ordered_pair(sk3(relation_inverse_image(sk15,X0),X1),sk0(sk15,X0,relation_inverse_image(sk15,X0),sk3(relation_inverse_image(sk15,X0),X1))),sk15)
| subset(relation_inverse_image(sk15,X0),X1) ),
inference(resolution,[status(thm)],[c13,p69]) ).
cnf(p199,plain,
( subset(relation_inverse_image(sk15,X0),X1)
| in(sk3(relation_inverse_image(sk15,X0),X1),relation_dom(sk15)) ),
inference(resolution,[status(thm)],[p197,p160]) ).
cnf(c14,plain,
( ~ in(sk3(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p201,plain,
( subset(relation_inverse_image(sk15,X0),relation_dom(sk15))
| subset(relation_inverse_image(sk15,X0),relation_dom(sk15)) ),
inference(resolution,[status(thm)],[p199,c14]) ).
cnf(p203,plain,
subset(relation_inverse_image(sk15,X0),relation_dom(sk15)),
inference(factoring,[status(thm)],[p201]) ).
cnf(c53,plain,
~ subset(relation_inverse_image(sk15,sk14),relation_dom(sk15)),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p204,plain,
$false,
inference(resolution,[status(thm)],[p203,c53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU209+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n001.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 13:16:53 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 29.18/4.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.18/4.30 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------