%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU072+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 02:50:54 PM UTC 2026
% Result : Theorem 12.52s 13.55s
% Output : Proof 12.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 67 ( 6 unt; 0 def)
% Number of atoms : 248 ( 74 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 282 ( 101 ~; 125 |; 40 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-3 aty)
% Number of variables : 85 ( 0 sgn 51 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f32,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f32_nnf,plain,
! [A,B] :
( ( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [A,B] :
( ( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c65,plain,
( X0 = singleton(X1)
| X0 = empty_set
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
fof(f27,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( in(A,relation_dom(B))
=> relation_image(B,singleton(A)) = singleton(apply(B,A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_funct_1) ).
fof(f27_nnf,plain,
! [A,B] :
( relation_image(B,singleton(A)) = singleton(apply(B,A))
| ~ in(A,relation_dom(B))
| ~ function(B)
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [B,A] :
( relation_image(B,singleton(A)) = singleton(apply(B,A))
| ~ in(A,relation_dom(B))
| ~ function(B)
| ~ relation(B) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c56,plain,
( relation_image(X1,singleton(X0)) = singleton(apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
fof(f29,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( ! [B] : subset(relation_inverse_image(A,relation_image(A,B)),B)
=> one_to_one(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t153_funct_1) ).
fof(f29_neg,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( ! [B] : subset(relation_inverse_image(A,relation_image(A,B)),B)
=> one_to_one(A) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f29_nnf,plain,
? [A] :
( ~ one_to_one(A)
& ! [B] : subset(relation_inverse_image(A,relation_image(A,B)),B)
& function(A)
& relation(A) ),
inference(nnf_transformation,[status(thm)],[f29_neg]) ).
fof(f29_sk,plain,
! [B] :
( ~ one_to_one(sk16)
& subset(relation_inverse_image(sk16,relation_image(sk16,B)),B)
& function(sk16)
& relation(sk16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16])],[f29_nnf]) ).
cnf(c59,plain,
relation(sk16),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p407,plain,
( relation_image(sk16,singleton(X0)) = singleton(apply(sk16,X0))
| ~ in(X0,relation_dom(sk16))
| ~ function(sk16) ),
inference(resolution,[status(thm)],[c56,c59]) ).
cnf(c60,plain,
function(sk16),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p414,plain,
( relation_image(sk16,singleton(X0)) = singleton(apply(sk16,X0))
| ~ in(X0,relation_dom(sk16)) ),
inference(resolution,[status(thm)],[p407,c60]) ).
fof(f5,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
=> B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f5_nnf,plain,
! [A] :
( ( ( ? [B,C] :
( B != C
& apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
| one_to_one(A) )
& ( ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C] :
( ( ( ( sk3(A) != sk4(A)
& apply(A,sk3(A)) = apply(A,sk4(A))
& in(sk4(A),relation_dom(A))
& in(sk3(A),relation_dom(A)) )
| one_to_one(A) )
& ( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A))
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f5_nnf]) ).
cnf(c16,plain,
( in(sk3(X0),relation_dom(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p230,plain,
( in(sk3(sk16),relation_dom(sk16))
| one_to_one(sk16)
| ~ function(sk16) ),
inference(resolution,[status(thm)],[c16,c59]) ).
cnf(p236,plain,
( in(sk3(sk16),relation_dom(sk16))
| one_to_one(sk16) ),
inference(resolution,[status(thm)],[p230,c60]) ).
cnf(p421,plain,
( one_to_one(sk16)
| relation_image(sk16,singleton(sk3(sk16))) = singleton(apply(sk16,sk3(sk16))) ),
inference(resolution,[status(thm)],[p414,p236]) ).
cnf(c61,plain,
subset(relation_inverse_image(sk16,relation_image(sk16,X1)),X1),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p434,plain,
( subset(relation_inverse_image(sk16,singleton(apply(sk16,sk3(sk16)))),singleton(sk3(sk16)))
| one_to_one(sk16) ),
inference(superposition,[status(thm)],[p421,c61]) ).
cnf(p509,plain,
( one_to_one(sk16)
| relation_inverse_image(sk16,singleton(apply(sk16,sk3(sk16)))) = singleton(sk3(sk16))
| relation_inverse_image(sk16,singleton(apply(sk16,sk3(sk16)))) = empty_set ),
inference(resolution,[status(thm)],[c65,p434]) ).
cnf(c18,plain,
( apply(X0,sk3(X0)) = apply(X0,sk4(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p257,plain,
( apply(sk16,sk3(sk16)) = apply(sk16,sk4(sk16))
| one_to_one(sk16)
| ~ function(sk16) ),
inference(resolution,[status(thm)],[c18,c59]) ).
cnf(p282,plain,
( apply(sk16,sk3(sk16)) = apply(sk16,sk4(sk16))
| one_to_one(sk16) ),
inference(resolution,[status(thm)],[p257,c60]) ).
cnf(c17,plain,
( in(sk4(X0),relation_dom(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p245,plain,
( in(sk4(sk16),relation_dom(sk16))
| one_to_one(sk16)
| ~ function(sk16) ),
inference(resolution,[status(thm)],[c17,c59]) ).
cnf(p251,plain,
( in(sk4(sk16),relation_dom(sk16))
| one_to_one(sk16) ),
inference(resolution,[status(thm)],[p245,c60]) ).
cnf(p422,plain,
( one_to_one(sk16)
| relation_image(sk16,singleton(sk4(sk16))) = singleton(apply(sk16,sk4(sk16))) ),
inference(resolution,[status(thm)],[p414,p251]) ).
cnf(p436,plain,
( one_to_one(sk16)
| relation_image(sk16,singleton(sk4(sk16))) = singleton(apply(sk16,sk3(sk16)))
| one_to_one(sk16) ),
inference(superposition,[status(thm)],[p282,p422]) ).
cnf(p467,plain,
( relation_image(sk16,singleton(sk4(sk16))) = singleton(apply(sk16,sk3(sk16)))
| one_to_one(sk16) ),
inference(factoring,[status(thm)],[p436]) ).
cnf(p468,plain,
( subset(relation_inverse_image(sk16,singleton(apply(sk16,sk3(sk16)))),singleton(sk4(sk16)))
| one_to_one(sk16) ),
inference(superposition,[status(thm)],[p467,c61]) ).
cnf(p1626,plain,
( subset(singleton(sk3(sk16)),singleton(sk4(sk16)))
| one_to_one(sk16)
| one_to_one(sk16)
| relation_inverse_image(sk16,singleton(apply(sk16,sk3(sk16)))) = empty_set ),
inference(superposition,[status(thm)],[p509,p468]) ).
cnf(p1633,plain,
( subset(singleton(sk3(sk16)),singleton(sk4(sk16)))
| one_to_one(sk16)
| relation_inverse_image(sk16,singleton(apply(sk16,sk3(sk16)))) = empty_set ),
inference(factoring,[status(thm)],[p1626]) ).
fof(f28,axiom,
! [A,B] :
( relation(B)
=> ( in(A,relation_rng(B))
<=> relation_inverse_image(B,singleton(A)) != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_funct_1) ).
fof(f28_nnf,plain,
! [A,B] :
( ( ( relation_inverse_image(B,singleton(A)) = empty_set
| in(A,relation_rng(B)) )
& ( relation_inverse_image(B,singleton(A)) != empty_set
| ~ in(A,relation_rng(B)) ) )
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [B,A] :
( ( ( relation_inverse_image(B,singleton(A)) = empty_set
| in(A,relation_rng(B)) )
& ( relation_inverse_image(B,singleton(A)) != empty_set
| ~ in(A,relation_rng(B)) ) )
| ~ relation(B) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c57,plain,
( relation_inverse_image(X1,singleton(X0)) != empty_set
| ~ in(X0,relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p438,plain,
( relation_inverse_image(sk16,singleton(X0)) != empty_set
| ~ in(X0,relation_rng(sk16)) ),
inference(resolution,[status(thm)],[c57,c59]) ).
fof(f4,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f4_nnf,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
& ~ in(C,B) )
| ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C,D] :
( ( ( ( sk1(A,B) = apply(A,sk2(A,B))
& in(sk2(A,B),relation_dom(A))
& ~ in(sk1(A,B),B) )
| ( ( sk1(A,B) != apply(A,D)
| ~ in(D,relation_dom(A)) )
& in(sk1(A,B),B) )
| B = relation_rng(A) )
& ( ( ( C != apply(A,D)
| ~ in(D,relation_dom(A))
| in(C,B) )
& ( ( C = apply(A,sk0(A,B,C))
& in(sk0(A,B,C),relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f4_nnf]) ).
cnf(c8,plain,
( X2 != apply(X0,X3)
| ~ in(X3,relation_dom(X0))
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p114,plain,
( X1 != apply(sk16,X2)
| ~ in(X2,relation_dom(sk16))
| in(X1,X0)
| X0 != relation_rng(sk16)
| ~ function(sk16) ),
inference(resolution,[status(thm)],[c8,c59]) ).
cnf(p121,plain,
( X0 != apply(sk16,X1)
| ~ in(X1,relation_dom(sk16))
| in(X0,relation_rng(sk16))
| ~ function(sk16) ),
inference(equality_resolution,[status(thm)],[p114]) ).
cnf(p124,plain,
( ~ in(X0,relation_dom(sk16))
| in(apply(sk16,X0),relation_rng(sk16))
| ~ function(sk16) ),
inference(equality_resolution,[status(thm)],[p121]) ).
cnf(p126,plain,
( ~ in(X0,relation_dom(sk16))
| in(apply(sk16,X0),relation_rng(sk16)) ),
inference(resolution,[status(thm)],[p124,c60]) ).
cnf(p238,plain,
( in(apply(sk16,sk3(sk16)),relation_rng(sk16))
| one_to_one(sk16) ),
inference(resolution,[status(thm)],[p236,p126]) ).
cnf(p449,plain,
( one_to_one(sk16)
| relation_inverse_image(sk16,singleton(apply(sk16,sk3(sk16)))) != empty_set ),
inference(resolution,[status(thm)],[p438,p238]) ).
cnf(p1634,plain,
( one_to_one(sk16)
| subset(singleton(sk3(sk16)),singleton(sk4(sk16)))
| one_to_one(sk16) ),
inference(resolution,[status(thm)],[p1633,p449]) ).
cnf(p1636,plain,
( subset(singleton(sk3(sk16)),singleton(sk4(sk16)))
| one_to_one(sk16) ),
inference(factoring,[status(thm)],[p1634]) ).
fof(f37,axiom,
! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f37_nnf,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [A,B] :
( A = B
| ~ subset(singleton(A),singleton(B)) ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c73,plain,
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(p1639,plain,
( sk3(sk16) = sk4(sk16)
| one_to_one(sk16) ),
inference(resolution,[status(thm)],[p1636,c73]) ).
cnf(c19,plain,
( sk3(X0) != sk4(X0)
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p271,plain,
( sk3(sk16) != sk4(sk16)
| one_to_one(sk16)
| ~ function(sk16) ),
inference(resolution,[status(thm)],[c19,c59]) ).
cnf(p277,plain,
( sk3(sk16) != sk4(sk16)
| one_to_one(sk16) ),
inference(resolution,[status(thm)],[p271,c60]) ).
cnf(p1640,plain,
( one_to_one(sk16)
| one_to_one(sk16) ),
inference(resolution,[status(thm)],[p1639,p277]) ).
cnf(p1641,plain,
one_to_one(sk16),
inference(factoring,[status(thm)],[p1640]) ).
cnf(c62,plain,
~ one_to_one(sk16),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p1642,plain,
$false,
inference(resolution,[status(thm)],[p1641,c62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU072+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/11.69 % Computer : n004.cluster.edu
% 0.18/11.69 % Model : x86_64 x86_64
% 0.18/11.69 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/11.69 % Memory : 8046.5625MB
% 0.18/11.69 % OS : Linux 6.8.0-71-generic
% 0.18/11.69 % CPULimit : 300
% 0.18/11.69 % WCLimit : 300
% 0.18/11.69 % DateTime : Thu Sep 24 12:41:33 UTC 2026
% 0.21/11.70 % CPUTime :
% 0.21/11.70 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 12.52/13.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.52/13.55 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------