%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU188+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 02:51:16 PM UTC 2026
% Result : Theorem 10.24s 6.86s
% Output : Proof 10.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 9 unt; 0 def)
% Number of atoms : 73 ( 23 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 70 ( 29 ~; 28 |; 6 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 15 ( 0 sgn 11 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f30,conjecture,
! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).
fof(f30_neg,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f30_nnf,plain,
? [A] :
( A != empty_set
& ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
& relation(A) ),
inference(nnf_transformation,[status(thm)],[f30_neg]) ).
fof(f30_sk,plain,
( sk13 != empty_set
& ( relation_rng(sk13) = empty_set
| relation_dom(sk13) = empty_set )
& relation(sk13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13])],[f30_nnf]) ).
cnf(c46,plain,
( relation_rng(sk13) = empty_set
| relation_dom(sk13) = empty_set ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f20,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f20_nnf,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c31,plain,
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(c45,plain,
relation(sk13),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(p267,plain,
( ~ empty(relation_rng(sk13))
| empty(sk13) ),
inference(resolution,[status(thm)],[c31,c45]) ).
cnf(p269,plain,
( ~ empty(empty_set)
| empty(sk13)
| relation_dom(sk13) = empty_set ),
inference(superposition,[status(thm)],[c46,p267]) ).
fof(f14,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f14_nnf,plain,
empty(empty_set),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c24,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(p270,plain,
( empty(sk13)
| relation_dom(sk13) = empty_set ),
inference(resolution,[status(thm)],[p269,c24]) ).
fof(f19,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_dom(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f19_nnf,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c30,plain,
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p265,plain,
( ~ empty(relation_dom(sk13))
| empty(sk13) ),
inference(resolution,[status(thm)],[c30,c45]) ).
cnf(p271,plain,
( ~ empty(empty_set)
| empty(sk13)
| empty(sk13) ),
inference(superposition,[status(thm)],[p270,p265]) ).
cnf(p272,plain,
( ~ empty(empty_set)
| empty(sk13) ),
inference(factoring,[status(thm)],[p271]) ).
cnf(p273,plain,
empty(sk13),
inference(resolution,[status(thm)],[p272,c24]) ).
fof(f31,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f31_nnf,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c48,plain,
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p278,plain,
sk13 = empty_set,
inference(resolution,[status(thm)],[p273,c48]) ).
cnf(c47,plain,
sk13 != empty_set,
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(p279,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[p278,c47]) ).
cnf(p280,plain,
$false,
inference(equality_resolution,[status(thm)],[p279]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU188+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.36 % Computer : n015.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Thu Sep 24 13:09:47 UTC 2026
% 0.10/5.36 % CPUTime :
% 0.10/5.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.24/6.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.24/6.86 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------