%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU010+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 02:19:04 PM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 8 unt; 5 def)
% Number of atoms : 90 ( 22 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 85 ( 34 ~; 32 |; 8 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 23 ( 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( relation_composition(A,identity_relation(relation_rng(A))) = A
& relation_composition(identity_relation(relation_dom(A)),A) = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( relation_composition(A,identity_relation(relation_rng(A))) = A
& relation_composition(identity_relation(relation_dom(A)),A) = A ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,axiom,
! [A,B] :
( relation(B)
=> ( subset(relation_dom(B),A)
=> relation_composition(identity_relation(A),B) = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A,B] :
( relation(B)
=> ( subset(relation_rng(B),A)
=> relation_composition(B,identity_relation(A)) = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f89,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f90,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f127,plain,
? [A] :
( ( relation_composition(A,identity_relation(relation_rng(A))) != A
| relation_composition(identity_relation(relation_dom(A)),A) != A )
& function(A)
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f128,plain,
( ( relation_composition(sK9_skl,identity_relation(relation_rng(sK9_skl))) != sK9_skl
| relation_composition(identity_relation(relation_dom(sK9_skl)),sK9_skl) != sK9_skl )
& function(sK9_skl)
& relation(sK9_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(A,sK9_skl)],[f127]) ).
fof(f129,plain,
relation(sK9_skl),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f131,plain,
( relation_composition(sK9_skl,identity_relation(relation_rng(sK9_skl))) != sK9_skl
| relation_composition(identity_relation(relation_dom(sK9_skl)),sK9_skl) != sK9_skl ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f132,plain,
! [A,B] :
( relation_composition(identity_relation(A),B) = B
| ~ subset(relation_dom(B),A)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f133,plain,
! [B] :
( ! [A] :
( relation_composition(identity_relation(A),B) = B
| ~ subset(relation_dom(B),A) )
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f132]) ).
fof(f134,plain,
! [X0,X1] :
( relation_composition(identity_relation(X1),X0) = X0
| ~ subset(relation_dom(X0),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
! [A,B] :
( relation_composition(B,identity_relation(A)) = B
| ~ subset(relation_rng(B),A)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f136,plain,
! [B] :
( ! [A] :
( relation_composition(B,identity_relation(A)) = B
| ~ subset(relation_rng(B),A) )
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f135]) ).
fof(f137,plain,
! [X0,X1] :
( relation_composition(X0,identity_relation(X1)) = X0
| ~ subset(relation_rng(X0),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f138,definition,
( sQ0_spl
<=> relation_composition(identity_relation(relation_dom(sK9_skl)),sK9_skl) = sK9_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( sQ0_spl
| relation_composition(identity_relation(relation_dom(sK9_skl)),sK9_skl) != sK9_skl ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f141,definition,
( sQ1_spl
<=> relation_composition(sK9_skl,identity_relation(relation_rng(sK9_skl))) = sK9_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f143,plain,
( sQ1_spl
| relation_composition(sK9_skl,identity_relation(relation_rng(sK9_skl))) != sK9_skl ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f131,f138,f141]) ).
fof(f161,plain,
( sQ0_spl
| ~ subset(relation_dom(sK9_skl),relation_dom(sK9_skl))
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f134,f140]) ).
fof(f162,definition,
( sQ2_spl
<=> relation(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f164,plain,
( sQ2_spl
| ~ relation(sK9_skl) ),
inference(component_clause,[status(thm)],[f162]) ).
fof(f165,definition,
( sQ3_spl
<=> subset(relation_dom(sK9_skl),relation_dom(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( sQ3_spl
| ~ subset(relation_dom(sK9_skl),relation_dom(sK9_skl)) ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f161,f162,f165,f138]) ).
fof(f169,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f167,f90]) ).
fof(f170,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f169]) ).
fof(f171,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f164,f129]) ).
fof(f172,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f171]) ).
fof(f206,plain,
( sQ1_spl
| ~ subset(relation_rng(sK9_skl),relation_rng(sK9_skl))
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f137,f143]) ).
fof(f207,definition,
( sQ9_spl
<=> subset(relation_rng(sK9_skl),relation_rng(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( sQ9_spl
| ~ subset(relation_rng(sK9_skl),relation_rng(sK9_skl)) ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f210,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f206,f162,f207,f141]) ).
fof(f211,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f209,f90]) ).
fof(f212,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f211]) ).
fof(f213,plain,
$false,
inference(sat_refutation,[status(thm)],[f144,f168,f170,f172,f210,f212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU010+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n003.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 05:48:31 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 0.16/0.46 % Refutation found
% 0.16/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.49 % Elapsed time: 0.059951 seconds
% 0.16/0.49 % CPU time: 0.139019 seconds
% 0.16/0.49 % Total memory used: 41.058 MB
% 0.16/0.49 % Net memory used: 41.019 MB
%------------------------------------------------------------------------------