%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU019+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 02:50:50 PM UTC 2026
% Result : Theorem 20.80s 3.10s
% Output : Proof 20.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 13 unt; 0 def)
% Number of atoms : 155 ( 47 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 166 ( 61 ~; 77 |; 22 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 68 ( 3 sgn 26 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( B = identity_relation(A)
<=> ( ! [C] :
( in(C,A)
=> apply(B,C) = C )
& relation_dom(B) = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f24_nnf,plain,
! [A,B] :
( ( ( ? [C] :
( apply(B,C) != C
& in(C,A) )
| relation_dom(B) != A
| B = identity_relation(A) )
& ( ( ! [C] :
( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [B,A,C] :
( ( ( ( apply(B,sk11(A,B)) != sk11(A,B)
& in(sk11(A,B),A) )
| relation_dom(B) != A
| B = identity_relation(A) )
& ( ( ( apply(B,C) = C
| ~ in(C,A) )
& relation_dom(B) = A )
| B != identity_relation(A) ) )
| ~ function(B)
| ~ relation(B) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f24_nnf]) ).
cnf(c40,plain,
( apply(X1,X2) = X2
| ~ in(X2,X0)
| X1 != identity_relation(X0)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p221,plain,
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[status(thm)],[c40]) ).
fof(f4,axiom,
! [A] : relation(identity_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f4_nnf,plain,
! [A] : relation(identity_relation(A)),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A] : relation(identity_relation(A)),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c8,plain,
relation(identity_relation(X0)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p377,plain,
( apply(identity_relation(X0),X1) = X1
| ~ in(X1,X0)
| ~ function(identity_relation(X0)) ),
inference(resolution,[status(thm)],[p221,c8]) ).
fof(f9,axiom,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f9_nnf,plain,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c16,plain,
function(identity_relation(X0)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p956,plain,
( apply(identity_relation(X1),X0) = X0
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[p377,c16]) ).
cnf(c39,plain,
( relation_dom(X1) = X0
| X1 != identity_relation(X0)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p193,plain,
( relation_dom(identity_relation(X0)) = X0
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[status(thm)],[c39]) ).
cnf(p360,plain,
( relation_dom(identity_relation(X0)) = X0
| ~ function(identity_relation(X0)) ),
inference(resolution,[status(thm)],[p193,c8]) ).
cnf(p361,plain,
relation_dom(identity_relation(X0)) = X0,
inference(resolution,[status(thm)],[p360,c16]) ).
fof(f3,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/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f3_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)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C] :
( ( ( ( sk0(A) != sk1(A)
& apply(A,sk0(A)) = apply(A,sk1(A))
& in(sk1(A),relation_dom(A))
& in(sk0(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,[sk0,sk1])],[f3_nnf]) ).
cnf(c4,plain,
( in(sk0(X0),relation_dom(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p69,plain,
( in(sk0(identity_relation(X0)),relation_dom(identity_relation(X0)))
| one_to_one(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(resolution,[status(thm)],[c8,c4]) ).
cnf(p332,plain,
( in(sk0(identity_relation(X0)),relation_dom(identity_relation(X0)))
| one_to_one(identity_relation(X0)) ),
inference(resolution,[status(thm)],[p69,c16]) ).
cnf(p367,plain,
( in(sk0(identity_relation(X0)),X0)
| one_to_one(identity_relation(X0)) ),
inference(demodulation,[status(thm)],[p361,p332]) ).
cnf(p963,plain,
( one_to_one(identity_relation(X0))
| apply(identity_relation(X0),sk0(identity_relation(X0))) = sk0(identity_relation(X0)) ),
inference(resolution,[status(thm)],[p956,p367]) ).
cnf(c6,plain,
( apply(X0,sk0(X0)) = apply(X0,sk1(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p85,plain,
( apply(identity_relation(X0),sk0(identity_relation(X0))) = apply(identity_relation(X0),sk1(identity_relation(X0)))
| one_to_one(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(resolution,[status(thm)],[c6,c8]) ).
cnf(p348,plain,
( apply(identity_relation(X0),sk0(identity_relation(X0))) = apply(identity_relation(X0),sk1(identity_relation(X0)))
| one_to_one(identity_relation(X0)) ),
inference(resolution,[status(thm)],[p85,c16]) ).
cnf(p2297,plain,
( sk0(identity_relation(X0)) = apply(identity_relation(X0),sk1(identity_relation(X0)))
| one_to_one(identity_relation(X0))
| one_to_one(identity_relation(X0)) ),
inference(superposition,[status(thm)],[p963,p348]) ).
cnf(p7336,plain,
( sk0(identity_relation(X0)) = apply(identity_relation(X0),sk1(identity_relation(X0)))
| one_to_one(identity_relation(X0)) ),
inference(factoring,[status(thm)],[p2297]) ).
cnf(c5,plain,
( in(sk1(X0),relation_dom(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p76,plain,
( in(sk1(identity_relation(X0)),relation_dom(identity_relation(X0)))
| one_to_one(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(resolution,[status(thm)],[c5,c8]) ).
cnf(p334,plain,
( in(sk1(identity_relation(X0)),relation_dom(identity_relation(X0)))
| one_to_one(identity_relation(X0)) ),
inference(resolution,[status(thm)],[p76,c16]) ).
cnf(p368,plain,
( in(sk1(identity_relation(X0)),X0)
| one_to_one(identity_relation(X0)) ),
inference(demodulation,[status(thm)],[p361,p334]) ).
cnf(p964,plain,
( one_to_one(identity_relation(X0))
| apply(identity_relation(X0),sk1(identity_relation(X0))) = sk1(identity_relation(X0)) ),
inference(resolution,[status(thm)],[p956,p368]) ).
cnf(p7338,plain,
( one_to_one(identity_relation(X0))
| sk0(identity_relation(X0)) = sk1(identity_relation(X0))
| one_to_one(identity_relation(X0)) ),
inference(superposition,[status(thm)],[p7336,p964]) ).
cnf(p7464,plain,
( sk0(identity_relation(X0)) = sk1(identity_relation(X0))
| one_to_one(identity_relation(X0)) ),
inference(factoring,[status(thm)],[p7338]) ).
cnf(c7,plain,
( sk0(X0) != sk1(X0)
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p96,plain,
( sk0(identity_relation(X0)) != sk1(identity_relation(X0))
| one_to_one(identity_relation(X0))
| ~ function(identity_relation(X0)) ),
inference(resolution,[status(thm)],[c7,c8]) ).
cnf(p355,plain,
( sk0(identity_relation(X0)) != sk1(identity_relation(X0))
| one_to_one(identity_relation(X0)) ),
inference(resolution,[status(thm)],[p96,c16]) ).
cnf(p7465,plain,
( one_to_one(identity_relation(X0))
| one_to_one(identity_relation(X0)) ),
inference(resolution,[status(thm)],[p7464,p355]) ).
cnf(p7468,plain,
one_to_one(identity_relation(X0)),
inference(factoring,[status(thm)],[p7465]) ).
fof(f27,conjecture,
! [A] : one_to_one(identity_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funct_1) ).
fof(f27_neg,negated_conjecture,
~ ! [A] : one_to_one(identity_relation(A)),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f27_nnf,plain,
? [A] : ~ one_to_one(identity_relation(A)),
inference(nnf_transformation,[status(thm)],[f27_neg]) ).
fof(f27_sk,plain,
~ one_to_one(identity_relation(sk12)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12])],[f27_nnf]) ).
cnf(c46,plain,
~ one_to_one(identity_relation(sk12)),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p7469,plain,
$false,
inference(resolution,[status(thm)],[p7468,c46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU019+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n009.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 12:35:13 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 20.80/3.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.80/3.10 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------