%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU189+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Thu Sep 24 02:19:35 PM UTC 2026
% Result : Theorem 0.13s 5.62s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 8 unt; 0 def)
% Number of atoms : 85 ( 38 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 87 ( 38 ~; 32 |; 9 &)
% ( 2 <=>; 5 =>; 0 <=; 1 <~>)
% 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 : 13 ( 11 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_dom(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,conjecture,
! [A] :
( relation(A)
=> ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f25,axiom,
( relation_rng(empty_set) = empty_set
& relation_dom(empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f46,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f63,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f66,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f67,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
? [A] :
( ( relation_dom(A) = empty_set
<~> relation_rng(A) = empty_set )
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f69,plain,
? [A] :
( ( relation_rng(A) != empty_set
| relation_dom(A) != empty_set )
& ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
& relation(A) ),
inference(NNF_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
( ( relation_rng(sK5_skl) != empty_set
| relation_dom(sK5_skl) != empty_set )
& ( relation_rng(sK5_skl) = empty_set
| relation_dom(sK5_skl) = empty_set )
& relation(sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(A,sK5_skl)],[f69]) ).
fof(f71,plain,
relation(sK5_skl),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
( relation_rng(sK5_skl) = empty_set
| relation_dom(sK5_skl) = empty_set ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f73,plain,
( relation_rng(sK5_skl) != empty_set
| relation_dom(sK5_skl) != empty_set ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f74,plain,
relation_dom(empty_set) = empty_set,
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f75,plain,
relation_rng(empty_set) = empty_set,
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f84,plain,
( relation_dom(sK5_skl) = empty_set
| ~ empty(empty_set)
| ~ relation(sK5_skl)
| empty(sK5_skl) ),
inference(paramodulation,[status(thm)],[f72,f46]) ).
fof(f85,plain,
( relation_dom(sK5_skl) = empty_set
| ~ empty(empty_set)
| empty(sK5_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f71]) ).
fof(f93,plain,
( relation_dom(sK5_skl) = empty_set
| empty(sK5_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f85,f63]) ).
fof(f94,plain,
( empty(sK5_skl)
| ~ empty(empty_set)
| ~ relation(sK5_skl)
| empty(sK5_skl) ),
inference(paramodulation,[status(thm)],[f93,f44]) ).
fof(f95,plain,
( ~ empty(empty_set)
| ~ relation(sK5_skl)
| empty(sK5_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f94]) ).
fof(f96,plain,
( ~ empty(empty_set)
| empty(sK5_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f95,f71]) ).
fof(f97,plain,
empty(sK5_skl),
inference(forward_subsumption_resolution,[status(thm)],[f96,f63]) ).
fof(f98,plain,
sK5_skl = empty_set,
inference(resolution,[status(thm)],[f97,f67]) ).
fof(f100,plain,
( relation_rng(empty_set) != empty_set
| relation_dom(sK5_skl) != empty_set ),
inference(backward_demodulation,[status(thm)],[f98,f73]) ).
fof(f103,plain,
( relation_rng(empty_set) != empty_set
| relation_dom(empty_set) != empty_set ),
inference(forward_demodulation,[status(thm)],[f98,f100]) ).
fof(f104,plain,
( relation_rng(empty_set) != empty_set
| empty_set != empty_set ),
inference(forward_demodulation,[status(thm)],[f74,f103]) ).
fof(f105,plain,
( empty_set != empty_set
| empty_set != empty_set ),
inference(forward_demodulation,[status(thm)],[f75,f104]) ).
fof(f106,plain,
empty_set != empty_set,
inference(duplicate_literals_removal,[status(thm)],[f105]) ).
fof(f107,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU189+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.57 % Computer : n004.cluster.edu
% 0.09/5.57 % Model : x86_64 x86_64
% 0.09/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.57 % Memory : 8046.5625MB
% 0.09/5.57 % OS : Linux 6.8.0-71-generic
% 0.09/5.57 % CPULimit : 300
% 0.09/5.57 % WCLimit : 300
% 0.09/5.57 % DateTime : Mon Sep 21 05:56:27 UTC 2026
% 0.09/5.57 % CPUTime :
% 0.09/5.58 % Drodi V4.1.1
% 0.13/5.62 % Refutation found
% 0.13/5.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.65 % Elapsed time: 0.071417 seconds
% 0.13/5.65 % CPU time: 0.167567 seconds
% 0.13/5.65 % Total memory used: 101.820 MB
% 0.13/5.65 % Net memory used: 101.585 MB
%------------------------------------------------------------------------------