%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU220+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 0.10s 0.55s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 28
% Syntax : Number of formulae : 136 ( 23 unt; 17 def)
% Number of atoms : 468 ( 110 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 540 ( 208 ~; 212 |; 82 &)
% ( 20 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 17 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 122 ( 109 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( function(function_inverse(A))
& relation(function_inverse(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
? [A] :
( function(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(B))
=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,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(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/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,conjecture,
! [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(f38,negated_conjecture,
~ ! [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)) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f40,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f55,plain,
! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f77,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f78,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f80,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f81,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f86,plain,
( function(sK1_skl)
& relation(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(A,sK1_skl)],[f19]) ).
fof(f87,plain,
relation(sK1_skl),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f98,plain,
( function(sK5_skl)
& empty(sK5_skl)
& relation(sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(A,sK5_skl)],[f23]) ).
fof(f100,plain,
empty(sK5_skl),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f101,plain,
function(sK5_skl),
inference(cnf_transformation,[status(thm)],[f98]) ).
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(f121,plain,
! [A,B] :
( ! [C] :
( apply(relation_composition(B,C),A) = apply(C,apply(B,A))
| ~ in(A,relation_dom(B))
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f122,plain,
! [B] :
( ! [C] :
( ! [A] :
( apply(relation_composition(B,C),A) = apply(C,apply(B,A))
| ~ in(A,relation_dom(B)) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f121]) ).
fof(f123,plain,
! [X0,X1,X2] :
( apply(relation_composition(X0,X1),X2) = apply(X1,apply(X0,X2))
| ~ in(X2,relation_dom(X0))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f133,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)],[f35]) ).
fof(f134,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(f135,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)],[f133,f134]) ).
fof(f136,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)],[f135]) ).
fof(f137,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)],[f136]) ).
fof(f138,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))],[f137]) ).
fof(f140,plain,
! [X0,X1,X2,X3] :
( sP0_prd(X2,X3,X1,X0)
| X1 != function_inverse(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f146,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(f147,plain,
! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f149,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)],[f38]) ).
fof(f150,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)],[f149]) ).
fof(f151,plain,
( ( sK16_skl != apply(relation_composition(function_inverse(sK15_skl),sK15_skl),sK16_skl)
| sK16_skl != apply(sK15_skl,apply(function_inverse(sK15_skl),sK16_skl)) )
& in(sK16_skl,relation_rng(sK15_skl))
& one_to_one(sK15_skl)
& function(sK15_skl)
& relation(sK15_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl]),skolemize(B,sK15_skl),skolemize(A,sK16_skl)],[f150]) ).
fof(f152,plain,
relation(sK15_skl),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f153,plain,
function(sK15_skl),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f154,plain,
one_to_one(sK15_skl),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f155,plain,
in(sK16_skl,relation_rng(sK15_skl)),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f156,plain,
( sK16_skl != apply(relation_composition(function_inverse(sK15_skl),sK15_skl),sK16_skl)
| sK16_skl != apply(sK15_skl,apply(function_inverse(sK15_skl),sK16_skl)) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f160,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f161,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f168,plain,
! [A,B,C,D] :
( ( ( ( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& D = apply(B,C)
& in(C,relation_rng(A)) )
| sP0_prd(D,C,B,A) )
& ( ( C = apply(A,D)
& in(D,relation_dom(A)) )
| D != apply(B,C)
| ~ in(C,relation_rng(A))
| ~ sP0_prd(D,C,B,A) ) ),
inference(NNF_transformation,[status(thm)],[f134]) ).
fof(f169,plain,
( ! [A,B,C,D] :
( ( ( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
& D = apply(B,C)
& in(C,relation_rng(A)) )
| sP0_prd(D,C,B,A) )
& ! [A,B,C,D] :
( ( C = apply(A,D)
& in(D,relation_dom(A)) )
| D != apply(B,C)
| ~ in(C,relation_rng(A))
| ~ sP0_prd(D,C,B,A) ) ),
inference(miniscoping,[status(thm)],[f168]) ).
fof(f171,plain,
! [X0,X1,X2,X3] :
( X1 = apply(X3,X0)
| X0 != apply(X2,X1)
| ~ in(X1,relation_rng(X3))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f169]) ).
fof(f175,definition,
( sQ0_spl
<=> sK16_skl = apply(sK15_skl,apply(function_inverse(sK15_skl),sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( ~ sQ0_spl
| sK16_skl = apply(sK15_skl,apply(function_inverse(sK15_skl),sK16_skl)) ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f177,plain,
( sQ0_spl
| sK16_skl != apply(sK15_skl,apply(function_inverse(sK15_skl),sK16_skl)) ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,definition,
( sQ1_spl
<=> sK16_skl = apply(relation_composition(function_inverse(sK15_skl),sK15_skl),sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( sQ1_spl
| sK16_skl != apply(relation_composition(function_inverse(sK15_skl),sK15_skl),sK16_skl) ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f156,f175,f178]) ).
fof(f183,plain,
! [X0,X1,X2] :
( sP0_prd(X1,X2,function_inverse(X0),X0)
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f140]) ).
fof(f187,plain,
! [X0,X1,X2] :
( X1 = apply(X2,apply(X0,X1))
| ~ in(X1,relation_rng(X2))
| ~ sP0_prd(apply(X0,X1),X1,X0,X2) ),
inference(destructive_equality_resolution,[status(thm)],[f171]) ).
fof(f214,plain,
empty(relation_rng(sK5_skl)),
inference(resolution,[status(thm)],[f100,f81]) ).
fof(f327,plain,
! [X0] :
( ~ empty(X0)
| relation_dom(X0) = empty_set ),
inference(resolution,[status(thm)],[f161,f78]) ).
fof(f330,plain,
sK5_skl = empty_set,
inference(resolution,[status(thm)],[f161,f100]) ).
fof(f337,plain,
relation_rng(sK5_skl) = empty_set,
inference(resolution,[status(thm)],[f161,f214]) ).
fof(f380,plain,
relation_rng(sK5_skl) = sK5_skl,
inference(forward_demodulation,[status(thm)],[f330,f337]) ).
fof(f418,plain,
( relation_rng(sK15_skl) = relation_dom(function_inverse(sK15_skl))
| ~ function(sK15_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f147,f154]) ).
fof(f420,definition,
( sQ18_spl
<=> relation(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f422,plain,
( sQ18_spl
| ~ relation(sK9_skl) ),
inference(component_clause,[status(thm)],[f420]) ).
fof(f423,definition,
( sQ19_spl
<=> function(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f425,plain,
( sQ19_spl
| ~ function(sK9_skl) ),
inference(component_clause,[status(thm)],[f423]) ).
fof(f430,definition,
( sQ21_spl
<=> relation(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f432,plain,
( sQ21_spl
| ~ relation(sK15_skl) ),
inference(component_clause,[status(thm)],[f430]) ).
fof(f433,definition,
( sQ22_spl
<=> function(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( sQ22_spl
| ~ function(sK15_skl) ),
inference(component_clause,[status(thm)],[f433]) ).
fof(f436,definition,
( sQ23_spl
<=> relation_rng(sK15_skl) = relation_dom(function_inverse(sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f437,plain,
( ~ sQ23_spl
| relation_rng(sK15_skl) = relation_dom(function_inverse(sK15_skl)) ),
inference(component_clause,[status(thm)],[f436]) ).
fof(f439,plain,
( sQ23_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f418,f430,f433,f436]) ).
fof(f441,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f435,f153]) ).
fof(f442,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f441]) ).
fof(f443,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f432,f152]) ).
fof(f444,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f443]) ).
fof(f457,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f425,f112]) ).
fof(f458,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f457]) ).
fof(f459,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f422,f111]) ).
fof(f460,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f459]) ).
fof(f467,plain,
! [X0] :
( ~ empty(X0)
| relation_dom(X0) = sK5_skl ),
inference(forward_demodulation,[status(thm)],[f330,f327]) ).
fof(f470,plain,
relation_dom(sK5_skl) = sK5_skl,
inference(resolution,[status(thm)],[f467,f100]) ).
fof(f477,definition,
( sQ26_spl
<=> function(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f479,plain,
( sQ26_spl
| ~ function(sK5_skl) ),
inference(component_clause,[status(thm)],[f477]) ).
fof(f501,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f479,f101]) ).
fof(f502,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f501]) ).
fof(f534,plain,
! [X0,X1] :
( ~ sQ23_spl
| apply(relation_composition(function_inverse(sK15_skl),X0),X1) = apply(X0,apply(function_inverse(sK15_skl),X1))
| ~ in(X1,relation_rng(sK15_skl))
| ~ function(X0)
| ~ relation(X0)
| ~ function(function_inverse(sK15_skl))
| ~ relation(function_inverse(sK15_skl)) ),
inference(paramodulation,[status(thm)],[f437,f123]) ).
fof(f538,definition,
( sQ34_spl
<=> relation(function_inverse(sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f540,plain,
( sQ34_spl
| ~ relation(function_inverse(sK15_skl)) ),
inference(component_clause,[status(thm)],[f538]) ).
fof(f541,definition,
( sQ35_spl
<=> function(function_inverse(sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f543,plain,
( sQ35_spl
| ~ function(function_inverse(sK15_skl)) ),
inference(component_clause,[status(thm)],[f541]) ).
fof(f558,definition,
! [X0,X1] :
( sQ40_spl
<=> ( apply(relation_composition(function_inverse(sK15_skl),X0),X1) = apply(X0,apply(function_inverse(sK15_skl),X1))
| ~ in(X1,relation_rng(sK15_skl))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f559,plain,
! [X0,X1] :
( ~ sQ40_spl
| apply(relation_composition(function_inverse(sK15_skl),X0),X1) = apply(X0,apply(function_inverse(sK15_skl),X1))
| ~ in(X1,relation_rng(sK15_skl))
| ~ function(X0)
| ~ relation(X0) ),
inference(component_clause,[status(thm)],[f558]) ).
fof(f561,plain,
( ~ sQ23_spl
| sQ40_spl
| ~ sQ35_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f534,f538,f541,f558,f436]) ).
fof(f574,plain,
( sQ34_spl
| ~ function(sK15_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f540,f54]) ).
fof(f575,plain,
( sQ34_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f574,f430,f433,f538]) ).
fof(f576,plain,
( sQ35_spl
| ~ function(sK15_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f543,f55]) ).
fof(f578,plain,
( sQ35_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f576,f430,f433,f541]) ).
fof(f648,plain,
! [X0,X1,X2] :
( sP0_prd(X1,X2,function_inverse(X0),X0)
| ~ function(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f183,f54]) ).
fof(f660,definition,
( sQ47_spl
<=> one_to_one(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f662,plain,
( sQ47_spl
| ~ one_to_one(sK15_skl) ),
inference(component_clause,[status(thm)],[f660]) ).
fof(f669,plain,
( sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f662,f154]) ).
fof(f670,plain,
sQ47_spl,
inference(contradiction_clause,[status(thm)],[f669]) ).
fof(f773,plain,
! [X0,X1] :
( ~ function(function_inverse(X1))
| ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| X0 = apply(X1,apply(function_inverse(X1),X0))
| ~ in(X0,relation_rng(X1)) ),
inference(resolution,[status(thm)],[f187,f648]) ).
fof(f774,plain,
! [X0,X1] :
( ~ one_to_one(X1)
| ~ function(X1)
| ~ relation(X1)
| X0 = apply(X1,apply(function_inverse(X1),X0))
| ~ in(X0,relation_rng(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f773,f55]) ).
fof(f870,definition,
( sQ58_spl
<=> relation_dom(sK5_skl) = relation_rng(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f872,plain,
( sQ58_spl
| relation_dom(sK5_skl) != relation_rng(sK5_skl) ),
inference(component_clause,[status(thm)],[f870]) ).
fof(f881,plain,
( sQ58_spl
| sK5_skl != relation_rng(sK5_skl) ),
inference(forward_demodulation,[status(thm)],[f470,f872]) ).
fof(f882,plain,
( sQ58_spl
| sK5_skl != sK5_skl ),
inference(forward_demodulation,[status(thm)],[f380,f881]) ).
fof(f883,plain,
( sQ58_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f882]) ).
fof(f884,plain,
sQ58_spl,
inference(contradiction_clause,[status(thm)],[f883]) ).
fof(f945,plain,
! [X0] :
( ~ sQ40_spl
| apply(relation_composition(function_inverse(sK15_skl),X0),sK16_skl) = apply(X0,apply(function_inverse(sK15_skl),sK16_skl))
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f559,f155]) ).
fof(f957,plain,
( ~ sQ40_spl
| apply(relation_composition(function_inverse(sK15_skl),sK15_skl),sK16_skl) = apply(sK15_skl,apply(function_inverse(sK15_skl),sK16_skl))
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f945,f153]) ).
fof(f980,definition,
( sQ69_spl
<=> relation(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f982,plain,
( sQ69_spl
| ~ relation(sK1_skl) ),
inference(component_clause,[status(thm)],[f980]) ).
fof(f987,definition,
( sQ71_spl
<=> apply(relation_composition(function_inverse(sK15_skl),sK15_skl),sK16_skl) = apply(sK15_skl,apply(function_inverse(sK15_skl),sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f988,plain,
( ~ sQ71_spl
| apply(relation_composition(function_inverse(sK15_skl),sK15_skl),sK16_skl) = apply(sK15_skl,apply(function_inverse(sK15_skl),sK16_skl)) ),
inference(component_clause,[status(thm)],[f987]) ).
fof(f990,plain,
( ~ sQ40_spl
| sQ71_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f957,f430,f987,f558]) ).
fof(f992,plain,
( sQ69_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f982,f87]) ).
fof(f993,plain,
sQ69_spl,
inference(contradiction_clause,[status(thm)],[f992]) ).
fof(f1499,plain,
! [X0] :
( ~ function(sK15_skl)
| ~ relation(sK15_skl)
| X0 = apply(sK15_skl,apply(function_inverse(sK15_skl),X0))
| ~ in(X0,relation_rng(sK15_skl)) ),
inference(resolution,[status(thm)],[f774,f154]) ).
fof(f1505,definition,
! [X0] :
( sQ111_spl
<=> ( X0 = apply(sK15_skl,apply(function_inverse(sK15_skl),X0))
| ~ in(X0,relation_rng(sK15_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f1506,plain,
! [X0] :
( ~ sQ111_spl
| X0 = apply(sK15_skl,apply(function_inverse(sK15_skl),X0))
| ~ in(X0,relation_rng(sK15_skl)) ),
inference(component_clause,[status(thm)],[f1505]) ).
fof(f1508,plain,
( ~ sQ22_spl
| ~ sQ21_spl
| sQ111_spl ),
inference(split_clause,[status(thm)],[f1499,f1505,f430,f433]) ).
fof(f1767,plain,
( ~ sQ111_spl
| sK16_skl = apply(sK15_skl,apply(function_inverse(sK15_skl),sK16_skl)) ),
inference(resolution,[status(thm)],[f1506,f155]) ).
fof(f1772,plain,
( ~ sQ111_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1767,f177]) ).
fof(f1773,plain,
( ~ sQ111_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1772]) ).
fof(f1774,plain,
( sQ1_spl
| ~ sQ71_spl
| sK16_skl != apply(sK15_skl,apply(function_inverse(sK15_skl),sK16_skl)) ),
inference(forward_demodulation,[status(thm)],[f988,f180]) ).
fof(f1811,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ sQ71_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f176,f1774]) ).
fof(f1812,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ sQ71_spl ),
inference(contradiction_clause,[status(thm)],[f1811]) ).
fof(f1813,plain,
$false,
inference(sat_refutation,[status(thm)],[f181,f439,f442,f444,f458,f460,f502,f561,f575,f578,f670,f884,f990,f993,f1508,f1773,f1812]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU220+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:58:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.55 % Refutation found
% 0.10/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.05/0.58 % Elapsed time: 0.186632 seconds
% 1.05/0.58 % CPU time: 1.294563 seconds
% 1.05/0.58 % Total memory used: 110.361 MB
% 1.05/0.58 % Net memory used: 108.404 MB
%------------------------------------------------------------------------------