%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU020+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 02:19:06 PM UTC 2026
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 58 ( 17 unt; 8 def)
% Number of atoms : 160 ( 18 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 162 ( 60 ~; 61 |; 23 &)
% ( 8 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 9 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 20 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f29,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( relation_dom(relation_composition(B,A)) = relation_dom(B)
=> subset(relation_rng(B),relation_dom(A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( subset(relation_rng(B),relation_dom(A))
& one_to_one(relation_composition(B,A)) )
=> one_to_one(B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [A] : one_to_one(identity_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( ? [B] :
( relation_composition(A,B) = identity_relation(relation_dom(A))
& function(B)
& relation(B) )
=> one_to_one(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( ? [B] :
( relation_composition(A,B) = identity_relation(relation_dom(A))
& function(B)
& relation(B) )
=> one_to_one(A) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f39,axiom,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f109,plain,
! [A] :
( ! [B] :
( subset(relation_rng(B),relation_dom(A))
| relation_dom(relation_composition(B,A)) != relation_dom(B)
| ~ function(B)
| ~ relation(B) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f110,plain,
! [X0,X1] :
( subset(relation_rng(X1),relation_dom(X0))
| relation_dom(relation_composition(X1,X0)) != relation_dom(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f117,plain,
! [A] :
( ! [B] :
( one_to_one(B)
| ~ subset(relation_rng(B),relation_dom(A))
| ~ one_to_one(relation_composition(B,A))
| ~ function(B)
| ~ relation(B) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f118,plain,
! [X0,X1] :
( one_to_one(X1)
| ~ subset(relation_rng(X1),relation_dom(X0))
| ~ one_to_one(relation_composition(X1,X0))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f122,plain,
! [X0] : one_to_one(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f123,plain,
? [A] :
( ~ one_to_one(A)
& ? [B] :
( relation_composition(A,B) = identity_relation(relation_dom(A))
& function(B)
& relation(B) )
& function(A)
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f124,plain,
( ~ one_to_one(sK9_skl)
& relation_composition(sK9_skl,sK10_skl) = identity_relation(relation_dom(sK9_skl))
& function(sK10_skl)
& relation(sK10_skl)
& function(sK9_skl)
& relation(sK9_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl]),skolemize(A,sK9_skl),skolemize(B,sK10_skl)],[f123]) ).
fof(f125,plain,
relation(sK9_skl),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f126,plain,
function(sK9_skl),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f127,plain,
relation(sK10_skl),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f128,plain,
function(sK10_skl),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f129,plain,
relation_composition(sK9_skl,sK10_skl) = identity_relation(relation_dom(sK9_skl)),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f130,plain,
~ one_to_one(sK9_skl),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f136,plain,
( ! [A] : relation_rng(identity_relation(A)) = A
& ! [A] : relation_dom(identity_relation(A)) = A ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f137,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f146,definition,
( sQ0_spl
<=> relation(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f148,plain,
( sQ0_spl
| ~ relation(sK9_skl) ),
inference(component_clause,[status(thm)],[f146]) ).
fof(f149,definition,
( sQ1_spl
<=> relation(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f151,plain,
( sQ1_spl
| ~ relation(sK10_skl) ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f186,definition,
( sQ4_spl
<=> function(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f188,plain,
( sQ4_spl
| ~ function(sK9_skl) ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,definition,
( sQ5_spl
<=> function(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( sQ5_spl
| ~ function(sK10_skl) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f196,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f148,f125]) ).
fof(f197,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f196]) ).
fof(f198,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f127]) ).
fof(f199,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f198]) ).
fof(f300,plain,
( one_to_one(sK9_skl)
| ~ subset(relation_rng(sK9_skl),relation_dom(sK10_skl))
| ~ one_to_one(identity_relation(relation_dom(sK9_skl)))
| ~ function(sK9_skl)
| ~ relation(sK9_skl)
| ~ function(sK10_skl)
| ~ relation(sK10_skl) ),
inference(paramodulation,[status(thm)],[f129,f118]) ).
fof(f301,definition,
( sQ16_spl
<=> one_to_one(identity_relation(relation_dom(sK9_skl))) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f303,plain,
( sQ16_spl
| ~ one_to_one(identity_relation(relation_dom(sK9_skl))) ),
inference(component_clause,[status(thm)],[f301]) ).
fof(f304,definition,
( sQ17_spl
<=> subset(relation_rng(sK9_skl),relation_dom(sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f306,plain,
( sQ17_spl
| ~ subset(relation_rng(sK9_skl),relation_dom(sK10_skl)) ),
inference(component_clause,[status(thm)],[f304]) ).
fof(f307,definition,
( sQ18_spl
<=> one_to_one(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f308,plain,
( ~ sQ18_spl
| one_to_one(sK9_skl) ),
inference(component_clause,[status(thm)],[f307]) ).
fof(f310,plain,
( sQ18_spl
| ~ sQ17_spl
| ~ sQ16_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f300,f149,f189,f146,f186,f301,f304,f307]) ).
fof(f311,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f188,f126]) ).
fof(f312,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f311]) ).
fof(f313,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f128]) ).
fof(f314,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f313]) ).
fof(f315,plain,
( ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f308,f130]) ).
fof(f316,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f315]) ).
fof(f317,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f303,f122]) ).
fof(f318,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f317]) ).
fof(f367,plain,
( sQ17_spl
| relation_dom(relation_composition(sK9_skl,sK10_skl)) != relation_dom(sK9_skl)
| ~ function(sK9_skl)
| ~ relation(sK9_skl)
| ~ function(sK10_skl)
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f306,f110]) ).
fof(f368,definition,
( sQ22_spl
<=> relation_dom(relation_composition(sK9_skl,sK10_skl)) = relation_dom(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f370,plain,
( sQ22_spl
| relation_dom(relation_composition(sK9_skl,sK10_skl)) != relation_dom(sK9_skl) ),
inference(component_clause,[status(thm)],[f368]) ).
fof(f371,plain,
( sQ17_spl
| ~ sQ22_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f367,f149,f189,f146,f186,f368,f304]) ).
fof(f372,plain,
( sQ22_spl
| relation_dom(identity_relation(relation_dom(sK9_skl))) != relation_dom(sK9_skl) ),
inference(forward_demodulation,[status(thm)],[f129,f370]) ).
fof(f373,plain,
( sQ22_spl
| relation_dom(sK9_skl) != relation_dom(sK9_skl) ),
inference(forward_demodulation,[status(thm)],[f137,f372]) ).
fof(f374,plain,
( sQ22_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f373]) ).
fof(f375,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f374]) ).
fof(f376,plain,
$false,
inference(sat_refutation,[status(thm)],[f197,f199,f310,f312,f314,f316,f318,f371,f375]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU020+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n016.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 05:51:38 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.38 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.045739 seconds
% 0.12/0.43 % CPU time: 0.139186 seconds
% 0.12/0.43 % Total memory used: 103.456 MB
% 0.12/0.43 % Net memory used: 103.381 MB
%------------------------------------------------------------------------------