%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU026+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 : 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 02:19:06 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 20
% Syntax : Number of formulae : 80 ( 15 unt; 12 def)
% Number of atoms : 217 ( 39 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 229 ( 92 ~; 90 |; 22 &)
% ( 12 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 19 ( 17 usr; 13 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 32 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( function(function_inverse(A))
& relation(function_inverse(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_rng(A),relation_dom(B))
=> relation_dom(relation_composition(A,B)) = relation_dom(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(relation_dom(A),relation_rng(B))
=> relation_rng(relation_composition(B,A)) = relation_rng(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_rng(relation_composition(function_inverse(A),A)) = relation_rng(A)
& relation_dom(relation_composition(function_inverse(A),A)) = relation_rng(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ( relation_rng(relation_composition(function_inverse(A),A)) = relation_rng(A)
& relation_dom(relation_composition(function_inverse(A),A)) = relation_rng(A) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f53,plain,
! [A] :
( ( function(function_inverse(A))
& relation(function_inverse(A)) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f54,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f102,plain,
( relation(sK6_skl)
& ~ empty(sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(A,sK6_skl)],[f24]) ).
fof(f104,plain,
relation(sK6_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f110,plain,
( one_to_one(sK9_skl)
& function(sK9_skl)
& relation(sK9_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(A,sK9_skl)],[f27]) ).
fof(f111,plain,
relation(sK9_skl),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f112,plain,
function(sK9_skl),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f117,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f118,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f127,plain,
! [A] :
( ! [B] :
( relation_dom(relation_composition(A,B)) = relation_dom(A)
| ~ subset(relation_rng(A),relation_dom(B))
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f128,plain,
! [X0,X1] :
( relation_dom(relation_composition(X0,X1)) = relation_dom(X0)
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f129,plain,
! [A] :
( ! [B] :
( relation_rng(relation_composition(B,A)) = relation_rng(A)
| ~ subset(relation_dom(A),relation_rng(B))
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f130,plain,
! [X0,X1] :
( relation_rng(relation_composition(X1,X0)) = relation_rng(X0)
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f134,plain,
! [A] :
( ( relation_dom(A) = relation_rng(function_inverse(A))
& relation_rng(A) = relation_dom(function_inverse(A)) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f135,plain,
! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f134]) ).
fof(f136,plain,
! [X0] :
( relation_dom(X0) = relation_rng(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f134]) ).
fof(f137,plain,
? [A] :
( ( relation_rng(relation_composition(function_inverse(A),A)) != relation_rng(A)
| relation_dom(relation_composition(function_inverse(A),A)) != relation_rng(A) )
& one_to_one(A)
& function(A)
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f138,plain,
( ( relation_rng(relation_composition(function_inverse(sK11_skl),sK11_skl)) != relation_rng(sK11_skl)
| relation_dom(relation_composition(function_inverse(sK11_skl),sK11_skl)) != relation_rng(sK11_skl) )
& one_to_one(sK11_skl)
& function(sK11_skl)
& relation(sK11_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(A,sK11_skl)],[f137]) ).
fof(f139,plain,
relation(sK11_skl),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f140,plain,
function(sK11_skl),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f141,plain,
one_to_one(sK11_skl),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f142,plain,
( relation_rng(relation_composition(function_inverse(sK11_skl),sK11_skl)) != relation_rng(sK11_skl)
| relation_dom(relation_composition(function_inverse(sK11_skl),sK11_skl)) != relation_rng(sK11_skl) ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f154,definition,
( sQ0_spl
<=> relation_dom(relation_composition(function_inverse(sK11_skl),sK11_skl)) = relation_rng(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f157,definition,
( sQ1_spl
<=> relation_rng(relation_composition(function_inverse(sK11_skl),sK11_skl)) = relation_rng(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f142,f154,f157]) ).
fof(f166,plain,
( relation_rng(sK11_skl) = relation_dom(function_inverse(sK11_skl))
| ~ function(sK11_skl)
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f135,f141]) ).
fof(f168,definition,
( sQ2_spl
<=> relation(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( sQ2_spl
| ~ relation(sK11_skl) ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,definition,
( sQ3_spl
<=> function(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( sQ3_spl
| ~ function(sK11_skl) ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,definition,
( sQ4_spl
<=> relation_rng(sK11_skl) = relation_dom(function_inverse(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( ~ sQ4_spl
| relation_rng(sK11_skl) = relation_dom(function_inverse(sK11_skl)) ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f166,f168,f171,f174]) ).
fof(f192,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f173,f140]) ).
fof(f193,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f192]) ).
fof(f194,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f139]) ).
fof(f195,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f194]) ).
fof(f198,definition,
( sQ8_spl
<=> relation(function_inverse(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( sQ8_spl
| ~ relation(function_inverse(sK11_skl)) ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f209,plain,
( sQ8_spl
| ~ function(sK11_skl)
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f200,f54]) ).
fof(f211,plain,
( sQ8_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f209,f168,f171,f198]) ).
fof(f212,plain,
( relation_dom(sK11_skl) = relation_rng(function_inverse(sK11_skl))
| ~ function(sK11_skl)
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f136,f141]) ).
fof(f214,definition,
( sQ11_spl
<=> relation_dom(sK11_skl) = relation_rng(function_inverse(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f215,plain,
( ~ sQ11_spl
| relation_dom(sK11_skl) = relation_rng(function_inverse(sK11_skl)) ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f217,plain,
( sQ11_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f212,f168,f171,f214]) ).
fof(f237,definition,
( sQ14_spl
<=> relation(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f239,plain,
( sQ14_spl
| ~ relation(sK6_skl) ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f263,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f239,f104]) ).
fof(f264,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f263]) ).
fof(f337,definition,
( sQ31_spl
<=> relation(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f339,plain,
( sQ31_spl
| ~ relation(sK9_skl) ),
inference(component_clause,[status(thm)],[f337]) ).
fof(f340,definition,
( sQ32_spl
<=> function(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f342,plain,
( sQ32_spl
| ~ function(sK9_skl) ),
inference(component_clause,[status(thm)],[f340]) ).
fof(f351,plain,
( sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f342,f112]) ).
fof(f352,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f351]) ).
fof(f353,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f339,f111]) ).
fof(f354,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f353]) ).
fof(f465,plain,
! [X0] :
( ~ sQ11_spl
| relation_dom(relation_composition(function_inverse(sK11_skl),X0)) = relation_dom(function_inverse(sK11_skl))
| ~ subset(relation_dom(sK11_skl),relation_dom(X0))
| ~ relation(X0)
| ~ relation(function_inverse(sK11_skl)) ),
inference(paramodulation,[status(thm)],[f215,f128]) ).
fof(f496,definition,
! [X0] :
( sQ60_spl
<=> ( relation_dom(relation_composition(function_inverse(sK11_skl),X0)) = relation_dom(function_inverse(sK11_skl))
| ~ subset(relation_dom(sK11_skl),relation_dom(X0))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f497,plain,
! [X0] :
( ~ sQ60_spl
| relation_dom(relation_composition(function_inverse(sK11_skl),X0)) = relation_dom(function_inverse(sK11_skl))
| ~ subset(relation_dom(sK11_skl),relation_dom(X0))
| ~ relation(X0) ),
inference(component_clause,[status(thm)],[f496]) ).
fof(f499,plain,
( ~ sQ11_spl
| sQ60_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f465,f198,f496,f214]) ).
fof(f508,plain,
! [X0] :
( ~ sQ60_spl
| ~ sQ4_spl
| relation_dom(relation_composition(function_inverse(sK11_skl),X0)) = relation_rng(sK11_skl)
| ~ subset(relation_dom(sK11_skl),relation_dom(X0))
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f175,f497]) ).
fof(f516,plain,
! [X0] :
( ~ sQ11_spl
| relation_rng(relation_composition(function_inverse(sK11_skl),X0)) = relation_rng(X0)
| ~ subset(relation_dom(X0),relation_dom(sK11_skl))
| ~ relation(function_inverse(sK11_skl))
| ~ relation(X0) ),
inference(paramodulation,[status(thm)],[f215,f130]) ).
fof(f541,definition,
! [X0] :
( sQ69_spl
<=> ( relation_rng(relation_composition(function_inverse(sK11_skl),X0)) = relation_rng(X0)
| ~ subset(relation_dom(X0),relation_dom(sK11_skl))
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f542,plain,
! [X0] :
( ~ sQ69_spl
| relation_rng(relation_composition(function_inverse(sK11_skl),X0)) = relation_rng(X0)
| ~ subset(relation_dom(X0),relation_dom(sK11_skl))
| ~ relation(X0) ),
inference(component_clause,[status(thm)],[f541]) ).
fof(f544,plain,
( ~ sQ11_spl
| ~ sQ8_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f516,f541,f198,f214]) ).
fof(f595,plain,
( ~ sQ60_spl
| ~ sQ4_spl
| relation_dom(relation_composition(function_inverse(sK11_skl),sK11_skl)) = relation_rng(sK11_skl)
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f508,f118]) ).
fof(f598,plain,
( ~ sQ60_spl
| ~ sQ4_spl
| sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f595,f168,f154,f174,f496]) ).
fof(f916,plain,
( ~ sQ69_spl
| relation_rng(relation_composition(function_inverse(sK11_skl),sK11_skl)) = relation_rng(sK11_skl)
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f542,f118]) ).
fof(f920,plain,
( ~ sQ69_spl
| sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f916,f168,f157,f541]) ).
fof(f936,plain,
$false,
inference(sat_refutation,[status(thm)],[f160,f177,f193,f195,f211,f217,f264,f352,f354,f499,f544,f598,f920]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU026+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:47:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.45 % Elapsed time: 0.081833 seconds
% 0.09/0.45 % CPU time: 0.223396 seconds
% 0.09/0.45 % Total memory used: 37.993 MB
% 0.09/0.45 % Net memory used: 37.874 MB
%------------------------------------------------------------------------------