%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU062+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 : n018.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 28.77s 4.16s
% Output : Proof 28.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 4 unt; 0 def)
% Number of atoms : 65 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 71 ( 28 ~; 23 |; 12 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 23 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f24,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(f24_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)],[f24]) ).
fof(f24_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)],[f24_nnf]) ).
cnf(c43,plain,
( relation_inverse_image(X1,singleton(X0)) = empty_set
| in(X0,relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
fof(f25,conjecture,
! [A,B] :
( relation(B)
=> ( ! [C] :
~ ( relation_inverse_image(B,singleton(C)) = empty_set
& in(C,A) )
=> subset(A,relation_rng(B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_funct_1) ).
fof(f25_neg,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ( ! [C] :
~ ( relation_inverse_image(B,singleton(C)) = empty_set
& in(C,A) )
=> subset(A,relation_rng(B)) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f25_nnf,plain,
? [A,B] :
( ~ subset(A,relation_rng(B))
& ! [C] :
( relation_inverse_image(B,singleton(C)) != empty_set
| ~ in(C,A) )
& relation(B) ),
inference(nnf_transformation,[status(thm)],[f25_neg]) ).
fof(f25_sk,plain,
! [C] :
( ~ subset(sk12,relation_rng(sk13))
& ( relation_inverse_image(sk13,singleton(C)) != empty_set
| ~ in(C,sk12) )
& relation(sk13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12,sk13])],[f25_nnf]) ).
cnf(c44,plain,
relation(sk13),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p130,plain,
( relation_inverse_image(sk13,singleton(X0)) = empty_set
| in(X0,relation_rng(sk13)) ),
inference(resolution,[status(thm)],[c43,c44]) ).
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(sk0(A,B),B)
& in(sk0(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f4_nnf]) ).
cnf(c7,plain,
( in(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(c45,plain,
( relation_inverse_image(sk13,singleton(X2)) != empty_set
| ~ in(X2,sk12) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p68,plain,
( relation_inverse_image(sk13,singleton(sk0(sk12,X0))) != empty_set
| subset(sk12,X0) ),
inference(resolution,[status(thm)],[c7,c45]) ).
cnf(p145,plain,
( subset(sk12,X0)
| in(sk0(sk12,X0),relation_rng(sk13)) ),
inference(resolution,[status(thm)],[p130,p68]) ).
cnf(c8,plain,
( ~ in(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p147,plain,
( subset(sk12,relation_rng(sk13))
| subset(sk12,relation_rng(sk13)) ),
inference(resolution,[status(thm)],[p145,c8]) ).
cnf(p148,plain,
subset(sk12,relation_rng(sk13)),
inference(factoring,[status(thm)],[p147]) ).
cnf(c46,plain,
~ subset(sk12,relation_rng(sk13)),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p149,plain,
$false,
inference(resolution,[status(thm)],[p148,c46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU062+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n018.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 12:42:49 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 28.77/4.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.77/4.16 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------