%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU188+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 41 ( 8 unt; 5 def)
% Number of atoms : 96 ( 23 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 93 ( 38 ~; 37 |; 6 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 12 ( 11 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f57,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_dom(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f156,conjecture,
! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f157,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
=> A = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f156]) ).
fof(f160,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f367,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f383,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f66]) ).
fof(f384,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f383]) ).
fof(f385,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f67]) ).
fof(f386,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f385]) ).
fof(f621,plain,
? [A] :
( A != empty_set
& ( relation_rng(A) = empty_set
| relation_dom(A) = empty_set )
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f157]) ).
fof(f622,plain,
( sK49_skl != empty_set
& ( relation_rng(sK49_skl) = empty_set
| relation_dom(sK49_skl) = empty_set )
& relation(sK49_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49_skl]),skolemize(A,sK49_skl)],[f621]) ).
fof(f623,plain,
relation(sK49_skl),
inference(cnf_transformation,[status(thm)],[f622]) ).
fof(f624,plain,
( relation_rng(sK49_skl) = empty_set
| relation_dom(sK49_skl) = empty_set ),
inference(cnf_transformation,[status(thm)],[f622]) ).
fof(f625,plain,
sK49_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f622]) ).
fof(f631,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f160]) ).
fof(f632,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f631]) ).
fof(f671,definition,
( sQ0_spl
<=> relation_dom(sK49_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f672,plain,
( ~ sQ0_spl
| relation_dom(sK49_skl) = empty_set ),
inference(component_clause,[status(thm)],[f671]) ).
fof(f674,definition,
( sQ1_spl
<=> relation_rng(sK49_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f675,plain,
( ~ sQ1_spl
| relation_rng(sK49_skl) = empty_set ),
inference(component_clause,[status(thm)],[f674]) ).
fof(f677,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f624,f671,f674]) ).
fof(f752,plain,
( ~ sQ0_spl
| ~ empty(empty_set)
| ~ relation(sK49_skl)
| empty(sK49_skl) ),
inference(paramodulation,[status(thm)],[f672,f384]) ).
fof(f760,definition,
( sQ4_spl
<=> empty(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f762,plain,
( sQ4_spl
| ~ empty(empty_set) ),
inference(component_clause,[status(thm)],[f760]) ).
fof(f767,definition,
( sQ6_spl
<=> empty(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f768,plain,
( ~ sQ6_spl
| empty(sK49_skl) ),
inference(component_clause,[status(thm)],[f767]) ).
fof(f770,definition,
( sQ7_spl
<=> relation(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f772,plain,
( sQ7_spl
| ~ relation(sK49_skl) ),
inference(component_clause,[status(thm)],[f770]) ).
fof(f773,plain,
( ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f752,f767,f770,f760,f671]) ).
fof(f774,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f762,f367]) ).
fof(f775,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f774]) ).
fof(f776,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f772,f623]) ).
fof(f777,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f776]) ).
fof(f802,plain,
( ~ sQ1_spl
| ~ empty(empty_set)
| ~ relation(sK49_skl)
| empty(sK49_skl) ),
inference(paramodulation,[status(thm)],[f675,f386]) ).
fof(f806,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f802,f767,f770,f760,f674]) ).
fof(f893,plain,
( ~ sQ6_spl
| sK49_skl = empty_set ),
inference(resolution,[status(thm)],[f632,f768]) ).
fof(f906,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f893,f625]) ).
fof(f907,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f906]) ).
fof(f908,plain,
$false,
inference(sat_refutation,[status(thm)],[f677,f773,f775,f777,f806,f907]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU188+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n012.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
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:55:53 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.057083 seconds
% 0.12/0.41 % CPU time: 0.151722 seconds
% 0.12/0.41 % Total memory used: 114.058 MB
% 0.12/0.41 % Net memory used: 113.861 MB
%------------------------------------------------------------------------------