%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU221+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 02:19:45 PM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of formulae : 91 ( 9 unt; 13 def)
% Number of atoms : 389 ( 83 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 502 ( 204 ~; 205 |; 61 &)
% ( 18 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 19 ( 17 usr; 13 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-2 aty)
% Number of variables : 77 ( 68 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
=> B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( function(function_inverse(A))
& relation(function_inverse(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( B = function_inverse(A)
<=> ( ! [C,D] :
( ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
=> ( D = apply(B,C)
& in(C,relation_rng(A)) ) )
& ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
=> ( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
& relation_dom(B) = relation_rng(A) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( in(A,relation_rng(B))
& one_to_one(B) )
=> ( A = apply(relation_composition(function_inverse(B),B),A)
& A = apply(B,apply(function_inverse(B),A)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> one_to_one(function_inverse(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> one_to_one(function_inverse(A)) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f51,plain,
! [A] :
( ( one_to_one(A)
<=> ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f52,plain,
! [A] :
( ( ( ? [B,C] :
( B != C
& apply(A,B) = apply(A,C)
& in(C,relation_dom(A))
& in(B,relation_dom(A)) )
| one_to_one(A) )
& ( ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
! [A] :
( ( ( ( sK0_skl(A) != sK1_skl(A)
& apply(A,sK0_skl(A)) = apply(A,sK1_skl(A))
& in(sK1_skl(A),relation_dom(A))
& in(sK0_skl(A),relation_dom(A)) )
| one_to_one(A) )
& ( ! [B,C] :
( B = C
| apply(A,B) != apply(A,C)
| ~ in(C,relation_dom(A))
| ~ in(B,relation_dom(A)) )
| ~ one_to_one(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(B,sK0_skl(A)),skolemize(C,sK1_skl(A))],[f52]) ).
fof(f55,plain,
! [X0] :
( in(sK0_skl(X0),relation_dom(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f56,plain,
! [X0] :
( in(sK1_skl(X0),relation_dom(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f57,plain,
! [X0] :
( apply(X0,sK0_skl(X0)) = apply(X0,sK1_skl(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f58,plain,
! [X0] :
( sK0_skl(X0) != sK1_skl(X0)
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f59,plain,
! [A] :
( ( function(function_inverse(A))
& relation(function_inverse(A)) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f60,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f119,plain,
! [A] :
( ! [B] :
( ( B = function_inverse(A)
<=> ( ! [C,D] :
( ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
| C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
| D != apply(B,C)
| ~ in(C,relation_rng(A)) ) )
& relation_dom(B) = relation_rng(A) ) )
| ~ function(B)
| ~ relation(B) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f120,definition,
! [A,B,C,D] :
( sP0_prd(D,C,B,A)
<=> ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
| D != apply(B,C)
| ~ in(C,relation_rng(A)) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f121,plain,
! [A] :
( ! [B] :
( ( B = function_inverse(A)
<=> ( ! [C,D] :
( ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
| C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& sP0_prd(D,C,B,A) )
& relation_dom(B) = relation_rng(A) ) )
| ~ function(B)
| ~ relation(B) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(formula_renaming,[status(thm)],[f119,f120]) ).
fof(f122,plain,
! [A] :
( ! [B] :
( ( ( ? [C,D] :
( ( ( D != apply(B,C)
| ~ in(C,relation_rng(A)) )
& C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ sP0_prd(D,C,B,A) )
| relation_dom(B) != relation_rng(A)
| B = function_inverse(A) )
& ( ( ! [C,D] :
( ( ( D = apply(B,C)
& in(C,relation_rng(A)) )
| C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& sP0_prd(D,C,B,A) )
& relation_dom(B) = relation_rng(A) )
| B != function_inverse(A) ) )
| ~ function(B)
| ~ relation(B) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [A] :
( ! [B] :
( ( ( ? [C,D] :
( ( D != apply(B,C)
| ~ in(C,relation_rng(A)) )
& C = apply(A,D)
& in(D,relation_dom(A)) )
| ? [C,D] : ~ sP0_prd(D,C,B,A)
| relation_dom(B) != relation_rng(A)
| B = function_inverse(A) )
& ( ( ! [C,D] :
( ( D = apply(B,C)
& in(C,relation_rng(A)) )
| C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& ! [C,D] : sP0_prd(D,C,B,A)
& relation_dom(B) = relation_rng(A) )
| B != function_inverse(A) ) )
| ~ function(B)
| ~ relation(B) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f122]) ).
fof(f124,plain,
! [A] :
( ! [B] :
( ( ( ( ( sK14_skl(B,A) != apply(B,sK13_skl(B,A))
| ~ in(sK13_skl(B,A),relation_rng(A)) )
& sK13_skl(B,A) = apply(A,sK14_skl(B,A))
& in(sK14_skl(B,A),relation_dom(A)) )
| ~ sP0_prd(sK12_skl(B,A),sK11_skl(B,A),B,A)
| relation_dom(B) != relation_rng(A)
| B = function_inverse(A) )
& ( ( ! [C,D] :
( ( D = apply(B,C)
& in(C,relation_rng(A)) )
| C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& ! [C,D] : sP0_prd(D,C,B,A)
& relation_dom(B) = relation_rng(A) )
| B != function_inverse(A) ) )
| ~ function(B)
| ~ relation(B) )
| ~ one_to_one(A)
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl,sK14_skl]),skolemize(C,sK11_skl(B,A)),skolemize(D,sK12_skl(B,A)),skolemize(C,sK13_skl(B,A)),skolemize(D,sK14_skl(B,A))],[f123]) ).
fof(f125,plain,
! [X0,X1] :
( relation_dom(X1) = relation_rng(X0)
| X1 != function_inverse(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f132,plain,
! [A,B] :
( ( A = apply(relation_composition(function_inverse(B),B),A)
& A = apply(B,apply(function_inverse(B),A)) )
| ~ in(A,relation_rng(B))
| ~ one_to_one(B)
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f133,plain,
! [B] :
( ! [A] :
( ( A = apply(relation_composition(function_inverse(B),B),A)
& A = apply(B,apply(function_inverse(B),A)) )
| ~ in(A,relation_rng(B))
| ~ one_to_one(B) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f132]) ).
fof(f134,plain,
! [X0,X1] :
( X1 = apply(X0,apply(function_inverse(X0),X1))
| ~ in(X1,relation_rng(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f136,plain,
? [A] :
( ~ one_to_one(function_inverse(A))
& one_to_one(A)
& function(A)
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f137,plain,
( ~ one_to_one(function_inverse(sK15_skl))
& one_to_one(sK15_skl)
& function(sK15_skl)
& relation(sK15_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(A,sK15_skl)],[f136]) ).
fof(f138,plain,
relation(sK15_skl),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f139,plain,
function(sK15_skl),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f140,plain,
one_to_one(sK15_skl),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f141,plain,
~ one_to_one(function_inverse(sK15_skl)),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f157,plain,
! [X0] :
( relation_dom(function_inverse(X0)) = relation_rng(X0)
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f125]) ).
fof(f164,plain,
! [X0] :
( relation_dom(function_inverse(X0)) = relation_rng(X0)
| ~ function(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f157,f60]) ).
fof(f165,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| relation_dom(function_inverse(X0)) = relation_rng(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f164,f61]) ).
fof(f166,plain,
! [X0] :
( relation_dom(function_inverse(X0)) = relation_rng(X0)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f165]) ).
fof(f167,plain,
( relation_dom(function_inverse(sK15_skl)) = relation_rng(sK15_skl)
| ~ function(sK15_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f166,f140]) ).
fof(f168,definition,
( sQ0_spl
<=> relation(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( sQ0_spl
| ~ relation(sK15_skl) ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,definition,
( sQ1_spl
<=> function(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( sQ1_spl
| ~ function(sK15_skl) ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,definition,
( sQ2_spl
<=> relation_dom(function_inverse(sK15_skl)) = relation_rng(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( ~ sQ2_spl
| relation_dom(function_inverse(sK15_skl)) = relation_rng(sK15_skl) ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f167,f168,f171,f174]) ).
fof(f205,definition,
( sQ9_spl
<=> relation(function_inverse(sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( sQ9_spl
| ~ relation(function_inverse(sK15_skl)) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,definition,
( sQ10_spl
<=> function(function_inverse(sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f210,plain,
( sQ10_spl
| ~ function(function_inverse(sK15_skl)) ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,definition,
( sQ11_spl
<=> one_to_one(function_inverse(sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f212,plain,
( ~ sQ11_spl
| one_to_one(function_inverse(sK15_skl)) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f225,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f173,f139]) ).
fof(f226,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f225]) ).
fof(f227,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f138]) ).
fof(f228,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f227]) ).
fof(f229,plain,
( sQ10_spl
| ~ function(sK15_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f210,f61]) ).
fof(f231,plain,
( sQ10_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f229,f168,f171,f208]) ).
fof(f232,plain,
( sQ9_spl
| ~ function(sK15_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f207,f60]) ).
fof(f234,plain,
( sQ9_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f232,f168,f171,f205]) ).
fof(f267,plain,
( in(sK0_skl(function_inverse(sK15_skl)),relation_dom(function_inverse(sK15_skl)))
| ~ function(function_inverse(sK15_skl))
| ~ relation(function_inverse(sK15_skl)) ),
inference(resolution,[status(thm)],[f55,f141]) ).
fof(f269,definition,
( sQ17_spl
<=> in(sK0_skl(function_inverse(sK15_skl)),relation_dom(function_inverse(sK15_skl))) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f270,plain,
( ~ sQ17_spl
| in(sK0_skl(function_inverse(sK15_skl)),relation_dom(function_inverse(sK15_skl))) ),
inference(component_clause,[status(thm)],[f269]) ).
fof(f272,plain,
( sQ17_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f267,f205,f208,f269]) ).
fof(f274,plain,
( ~ sQ17_spl
| ~ sQ2_spl
| in(sK0_skl(function_inverse(sK15_skl)),relation_rng(sK15_skl)) ),
inference(forward_demodulation,[status(thm)],[f175,f270]) ).
fof(f275,plain,
( in(sK1_skl(function_inverse(sK15_skl)),relation_dom(function_inverse(sK15_skl)))
| ~ function(function_inverse(sK15_skl))
| ~ relation(function_inverse(sK15_skl)) ),
inference(resolution,[status(thm)],[f56,f141]) ).
fof(f277,definition,
( sQ18_spl
<=> in(sK1_skl(function_inverse(sK15_skl)),relation_dom(function_inverse(sK15_skl))) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f278,plain,
( ~ sQ18_spl
| in(sK1_skl(function_inverse(sK15_skl)),relation_dom(function_inverse(sK15_skl))) ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f280,plain,
( sQ18_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f275,f205,f208,f277]) ).
fof(f282,plain,
( ~ sQ18_spl
| ~ sQ2_spl
| in(sK1_skl(function_inverse(sK15_skl)),relation_rng(sK15_skl)) ),
inference(forward_demodulation,[status(thm)],[f175,f278]) ).
fof(f283,plain,
( ~ sQ17_spl
| ~ sQ2_spl
| sK0_skl(function_inverse(sK15_skl)) = apply(sK15_skl,apply(function_inverse(sK15_skl),sK0_skl(function_inverse(sK15_skl))))
| ~ one_to_one(sK15_skl)
| ~ function(sK15_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f274,f134]) ).
fof(f285,definition,
( sQ19_spl
<=> one_to_one(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( sQ19_spl
| ~ one_to_one(sK15_skl) ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f288,definition,
( sQ20_spl
<=> sK0_skl(function_inverse(sK15_skl)) = apply(sK15_skl,apply(function_inverse(sK15_skl),sK0_skl(function_inverse(sK15_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f289,plain,
( ~ sQ20_spl
| sK0_skl(function_inverse(sK15_skl)) = apply(sK15_skl,apply(function_inverse(sK15_skl),sK0_skl(function_inverse(sK15_skl)))) ),
inference(component_clause,[status(thm)],[f288]) ).
fof(f291,plain,
( ~ sQ17_spl
| ~ sQ2_spl
| sQ20_spl
| ~ sQ19_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f283,f168,f171,f285,f288,f174,f269]) ).
fof(f292,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f287,f140]) ).
fof(f293,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f292]) ).
fof(f321,plain,
( ~ sQ18_spl
| ~ sQ2_spl
| sK1_skl(function_inverse(sK15_skl)) = apply(sK15_skl,apply(function_inverse(sK15_skl),sK1_skl(function_inverse(sK15_skl))))
| ~ one_to_one(sK15_skl)
| ~ function(sK15_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f282,f134]) ).
fof(f323,definition,
( sQ27_spl
<=> sK1_skl(function_inverse(sK15_skl)) = apply(sK15_skl,apply(function_inverse(sK15_skl),sK1_skl(function_inverse(sK15_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f324,plain,
( ~ sQ27_spl
| sK1_skl(function_inverse(sK15_skl)) = apply(sK15_skl,apply(function_inverse(sK15_skl),sK1_skl(function_inverse(sK15_skl)))) ),
inference(component_clause,[status(thm)],[f323]) ).
fof(f326,plain,
( ~ sQ18_spl
| ~ sQ2_spl
| sQ27_spl
| ~ sQ19_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f321,f168,f171,f285,f323,f174,f277]) ).
fof(f381,plain,
( apply(function_inverse(sK15_skl),sK0_skl(function_inverse(sK15_skl))) = apply(function_inverse(sK15_skl),sK1_skl(function_inverse(sK15_skl)))
| ~ function(function_inverse(sK15_skl))
| ~ relation(function_inverse(sK15_skl)) ),
inference(resolution,[status(thm)],[f57,f141]) ).
fof(f383,definition,
( sQ37_spl
<=> apply(function_inverse(sK15_skl),sK0_skl(function_inverse(sK15_skl))) = apply(function_inverse(sK15_skl),sK1_skl(function_inverse(sK15_skl))) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f384,plain,
( ~ sQ37_spl
| apply(function_inverse(sK15_skl),sK0_skl(function_inverse(sK15_skl))) = apply(function_inverse(sK15_skl),sK1_skl(function_inverse(sK15_skl))) ),
inference(component_clause,[status(thm)],[f383]) ).
fof(f386,plain,
( sQ37_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f381,f205,f208,f383]) ).
fof(f545,plain,
( ~ sQ27_spl
| ~ sQ37_spl
| sK1_skl(function_inverse(sK15_skl)) = apply(sK15_skl,apply(function_inverse(sK15_skl),sK0_skl(function_inverse(sK15_skl)))) ),
inference(forward_demodulation,[status(thm)],[f384,f324]) ).
fof(f549,plain,
( ~ sQ27_spl
| ~ sQ37_spl
| ~ sQ20_spl
| sK1_skl(function_inverse(sK15_skl)) = sK0_skl(function_inverse(sK15_skl)) ),
inference(forward_demodulation,[status(thm)],[f289,f545]) ).
fof(f550,plain,
( ~ sQ27_spl
| ~ sQ37_spl
| ~ sQ20_spl
| one_to_one(function_inverse(sK15_skl))
| ~ function(function_inverse(sK15_skl))
| ~ relation(function_inverse(sK15_skl)) ),
inference(resolution,[status(thm)],[f549,f58]) ).
fof(f553,plain,
( ~ sQ27_spl
| ~ sQ37_spl
| ~ sQ20_spl
| sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f550,f205,f208,f211,f288,f383,f323]) ).
fof(f556,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f212,f141]) ).
fof(f557,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f556]) ).
fof(f558,plain,
$false,
inference(sat_refutation,[status(thm)],[f177,f226,f228,f231,f234,f272,f280,f291,f293,f326,f386,f553,f557]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU221+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n005.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 05:59:18 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.056208 seconds
% 0.14/0.43 % CPU time: 0.171034 seconds
% 0.14/0.43 % Total memory used: 83.743 MB
% 0.14/0.43 % Net memory used: 83.555 MB
%------------------------------------------------------------------------------