%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU227+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 : n009.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 02:51:24 PM UTC 2026
% Result : Theorem 25.96s 4.18s
% Output : Proof 25.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 5 unt; 0 def)
% Number of atoms : 192 ( 21 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 233 ( 84 ~; 92 |; 42 &)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 2 con; 0-4 aty)
% Number of variables : 118 ( 0 sgn 55 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,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(f8_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)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C,D] :
( ( ( ( in(ordered_pair(sk8(A,B),sk9(A,B)),A)
& ~ in(sk8(A,B),B) )
| ( ~ in(ordered_pair(sk8(A,B),D),A)
& in(sk8(A,B),B) )
| B = relation_dom(A) )
& ( ( ( ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( in(ordered_pair(C,sk7(A,B,C)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7,sk8,sk9])],[f8_nnf]) ).
cnf(c28,plain,
( in(ordered_pair(X2,sk7(X0,X1,X2)),X0)
| ~ in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f40,conjecture,
! [A,B] :
( relation(B)
=> ( subset(A,relation_dom(B))
=> subset(A,relation_inverse_image(B,relation_image(B,A))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t146_funct_1) ).
fof(f40_neg,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ( subset(A,relation_dom(B))
=> subset(A,relation_inverse_image(B,relation_image(B,A))) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f40_nnf,plain,
? [A,B] :
( ~ subset(A,relation_inverse_image(B,relation_image(B,A)))
& subset(A,relation_dom(B))
& relation(B) ),
inference(nnf_transformation,[status(thm)],[f40_neg]) ).
fof(f40_sk,plain,
( ~ subset(sk21,relation_inverse_image(sk22,relation_image(sk22,sk21)))
& subset(sk21,relation_dom(sk22))
& relation(sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk21,sk22])],[f40_nnf]) ).
cnf(c79,plain,
relation(sk22),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(p462,plain,
( in(ordered_pair(X1,sk7(sk22,X0,X1)),sk22)
| ~ in(X1,X0)
| X0 != relation_dom(sk22) ),
inference(resolution,[status(thm)],[c28,c79]) ).
cnf(p471,plain,
( in(ordered_pair(X0,sk7(sk22,relation_dom(sk22),X0)),sk22)
| ~ in(X0,relation_dom(sk22)) ),
inference(equality_resolution,[status(thm)],[p462]) ).
fof(f7,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f7_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)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk6(A,B),B)
& in(sk6(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk6])],[f7_nnf]) ).
cnf(c26,plain,
( in(sk6(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(c25,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(c80,plain,
subset(sk21,relation_dom(sk22)),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(p395,plain,
( in(X0,relation_dom(sk22))
| ~ in(X0,sk21) ),
inference(resolution,[status(thm)],[c25,c80]) ).
cnf(p441,plain,
( in(sk6(sk21,X0),relation_dom(sk22))
| subset(sk21,X0) ),
inference(resolution,[status(thm)],[c26,p395]) ).
cnf(p502,plain,
( subset(sk21,X0)
| in(ordered_pair(sk6(sk21,X0),sk7(sk22,relation_dom(sk22),sk6(sk21,X0))),sk22) ),
inference(resolution,[status(thm)],[p471,p441]) ).
fof(f6,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(f6_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)],[f6]) ).
fof(f6_sk,plain,
! [A,C,B,D,E] :
( ( ( ( in(sk5(A,B,C),B)
& in(ordered_pair(sk4(A,B,C),sk5(A,B,C)),A)
& ~ in(sk4(A,B,C),C) )
| ( ( ~ in(E,B)
| ~ in(ordered_pair(sk4(A,B,C),E),A) )
& in(sk4(A,B,C),C) )
| C = relation_inverse_image(A,B) )
& ( ( ( ~ in(E,B)
| ~ in(ordered_pair(D,E),A)
| in(D,C) )
& ( ( in(sk3(A,B,C,D),B)
& in(ordered_pair(D,sk3(A,B,C,D)),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4,sk5])],[f6_nnf]) ).
cnf(c18,plain,
( ~ in(X4,X1)
| ~ in(ordered_pair(X3,X4),X0)
| in(X3,X2)
| X2 != relation_inverse_image(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p263,plain,
( ~ in(X3,X1)
| ~ in(ordered_pair(X2,X3),sk22)
| in(X2,X0)
| X0 != relation_inverse_image(sk22,X1) ),
inference(resolution,[status(thm)],[c18,c79]) ).
cnf(p272,plain,
( ~ in(X2,X1)
| ~ in(ordered_pair(X0,X2),sk22)
| in(X0,relation_inverse_image(sk22,X1)) ),
inference(equality_resolution,[status(thm)],[p263]) ).
cnf(p509,plain,
( ~ in(sk7(sk22,relation_dom(sk22),sk6(sk21,X0)),X1)
| in(sk6(sk21,X0),relation_inverse_image(sk22,X1))
| subset(sk21,X0) ),
inference(resolution,[status(thm)],[p502,p272]) ).
fof(f5,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f5_nnf,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
& ~ in(D,C) )
| ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
& in(D,C) ) )
| C = relation_image(A,B) )
& ( ! [D] :
( ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| in(D,C) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,C,B,D,E] :
( ( ( ( in(sk2(A,B,C),B)
& in(ordered_pair(sk2(A,B,C),sk1(A,B,C)),A)
& ~ in(sk1(A,B,C),C) )
| ( ( ~ in(E,B)
| ~ in(ordered_pair(E,sk1(A,B,C)),A) )
& in(sk1(A,B,C),C) )
| C = relation_image(A,B) )
& ( ( ( ~ in(E,B)
| ~ in(ordered_pair(E,D),A)
| in(D,C) )
& ( ( in(sk0(A,B,C,D),B)
& in(ordered_pair(sk0(A,B,C,D),D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f5_nnf]) ).
cnf(c9,plain,
( ~ in(X4,X1)
| ~ in(ordered_pair(X4,X3),X0)
| in(X3,X2)
| X2 != relation_image(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p123,plain,
( ~ in(X3,X1)
| ~ in(ordered_pair(X3,X2),sk22)
| in(X2,X0)
| X0 != relation_image(sk22,X1) ),
inference(resolution,[status(thm)],[c9,c79]) ).
cnf(p131,plain,
( ~ in(X2,X1)
| ~ in(ordered_pair(X2,X0),sk22)
| in(X0,relation_image(sk22,X1)) ),
inference(equality_resolution,[status(thm)],[p123]) ).
cnf(p508,plain,
( ~ in(sk6(sk21,X0),X1)
| in(sk7(sk22,relation_dom(sk22),sk6(sk21,X0)),relation_image(sk22,X1))
| subset(sk21,X0) ),
inference(resolution,[status(thm)],[p502,p131]) ).
cnf(p612,plain,
( subset(sk21,X0)
| in(sk7(sk22,relation_dom(sk22),sk6(sk21,X0)),relation_image(sk22,sk21))
| subset(sk21,X0) ),
inference(resolution,[status(thm)],[p508,c26]) ).
cnf(p614,plain,
( in(sk7(sk22,relation_dom(sk22),sk6(sk21,X0)),relation_image(sk22,sk21))
| subset(sk21,X0) ),
inference(factoring,[status(thm)],[p612]) ).
cnf(p636,plain,
( subset(sk21,X0)
| in(sk6(sk21,X0),relation_inverse_image(sk22,relation_image(sk22,sk21)))
| subset(sk21,X0) ),
inference(resolution,[status(thm)],[p509,p614]) ).
cnf(p638,plain,
( in(sk6(sk21,X0),relation_inverse_image(sk22,relation_image(sk22,sk21)))
| subset(sk21,X0) ),
inference(factoring,[status(thm)],[p636]) ).
cnf(c27,plain,
( ~ in(sk6(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p642,plain,
( subset(sk21,relation_inverse_image(sk22,relation_image(sk22,sk21)))
| subset(sk21,relation_inverse_image(sk22,relation_image(sk22,sk21))) ),
inference(resolution,[status(thm)],[p638,c27]) ).
cnf(p644,plain,
subset(sk21,relation_inverse_image(sk22,relation_image(sk22,sk21))),
inference(factoring,[status(thm)],[p642]) ).
cnf(c81,plain,
~ subset(sk21,relation_inverse_image(sk22,relation_image(sk22,sk21))),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(p645,plain,
$false,
inference(resolution,[status(thm)],[p644,c81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU227+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 13:17:44 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 25.96/4.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.96/4.18 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------