%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU220+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 0.09s 0.47s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 27
% Syntax : Number of formulae : 130 ( 21 unt; 16 def)
% Number of atoms : 458 ( 109 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 534 ( 206 ~; 209 |; 82 &)
% ( 19 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 16 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 122 ( 109 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( function(function_inverse(A))
& relation(function_inverse(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
? [A] :
( function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f35,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(f36,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/sandbox/benchmark/theBenchmark.p') ).
fof(f37,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)],[f36]) ).
fof(f38,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,plain,
! [A] :
( ( function(function_inverse(A))
& relation(function_inverse(A)) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f52,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f74,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f75,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f77,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f78,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f83,plain,
( function(sK1_skl)
& relation(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(A,sK1_skl)],[f23]) ).
fof(f84,plain,
relation(sK1_skl),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f91,plain,
( function(sK4_skl)
& empty(sK4_skl)
& relation(sK4_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(A,sK4_skl)],[f26]) ).
fof(f93,plain,
empty(sK4_skl),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f100,plain,
( one_to_one(sK7_skl)
& function(sK7_skl)
& relation(sK7_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(A,sK7_skl)],[f29]) ).
fof(f101,plain,
relation(sK7_skl),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f102,plain,
function(sK7_skl),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f109,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)],[f32]) ).
fof(f110,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)],[f109]) ).
fof(f111,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)],[f110]) ).
fof(f114,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(f115,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(f116,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)],[f114,f115]) ).
fof(f117,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)],[f116]) ).
fof(f118,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)],[f117]) ).
fof(f119,plain,
! [A] :
( ! [B] :
( ( ( ( ( sK12_skl(B,A) != apply(B,sK11_skl(B,A))
| ~ in(sK11_skl(B,A),relation_rng(A)) )
& sK11_skl(B,A) = apply(A,sK12_skl(B,A))
& in(sK12_skl(B,A),relation_dom(A)) )
| ~ sP0_prd(sK10_skl(B,A),sK9_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,[sK9_skl,sK10_skl,sK11_skl,sK12_skl]),skolemize(C,sK9_skl(B,A)),skolemize(D,sK10_skl(B,A)),skolemize(C,sK11_skl(B,A)),skolemize(D,sK12_skl(B,A))],[f118]) ).
fof(f121,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)],[f119]) ).
fof(f127,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)],[f35]) ).
fof(f128,plain,
! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f130,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)],[f37]) ).
fof(f131,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)],[f130]) ).
fof(f132,plain,
( ( sK14_skl != apply(relation_composition(function_inverse(sK13_skl),sK13_skl),sK14_skl)
| sK14_skl != apply(sK13_skl,apply(function_inverse(sK13_skl),sK14_skl)) )
& in(sK14_skl,relation_rng(sK13_skl))
& one_to_one(sK13_skl)
& function(sK13_skl)
& relation(sK13_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(B,sK13_skl),skolemize(A,sK14_skl)],[f131]) ).
fof(f133,plain,
relation(sK13_skl),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f134,plain,
function(sK13_skl),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f135,plain,
one_to_one(sK13_skl),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f136,plain,
in(sK14_skl,relation_rng(sK13_skl)),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f137,plain,
( sK14_skl != apply(relation_composition(function_inverse(sK13_skl),sK13_skl),sK14_skl)
| sK14_skl != apply(sK13_skl,apply(function_inverse(sK13_skl),sK14_skl)) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f138,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f139,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f146,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)],[f115]) ).
fof(f147,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)],[f146]) ).
fof(f149,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)],[f147]) ).
fof(f153,definition,
( sQ0_spl
<=> sK14_skl = apply(sK13_skl,apply(function_inverse(sK13_skl),sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( sQ0_spl
| sK14_skl != apply(sK13_skl,apply(function_inverse(sK13_skl),sK14_skl)) ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,definition,
( sQ1_spl
<=> sK14_skl = apply(relation_composition(function_inverse(sK13_skl),sK13_skl),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( sQ1_spl
| sK14_skl != apply(relation_composition(function_inverse(sK13_skl),sK13_skl),sK14_skl) ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f159,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f137,f153,f156]) ).
fof(f161,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)],[f121]) ).
fof(f165,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)],[f149]) ).
fof(f197,plain,
empty(relation_rng(sK4_skl)),
inference(resolution,[status(thm)],[f93,f78]) ).
fof(f308,plain,
! [X0] :
( ~ empty(X0)
| relation_dom(X0) = empty_set ),
inference(resolution,[status(thm)],[f139,f75]) ).
fof(f310,plain,
sK4_skl = empty_set,
inference(resolution,[status(thm)],[f139,f93]) ).
fof(f316,plain,
relation_rng(sK4_skl) = empty_set,
inference(resolution,[status(thm)],[f139,f197]) ).
fof(f360,plain,
relation_rng(sK4_skl) = sK4_skl,
inference(forward_demodulation,[status(thm)],[f310,f316]) ).
fof(f374,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)],[f161,f52]) ).
fof(f385,plain,
( relation_rng(sK13_skl) = relation_dom(function_inverse(sK13_skl))
| ~ function(sK13_skl)
| ~ relation(sK13_skl) ),
inference(resolution,[status(thm)],[f128,f135]) ).
fof(f386,definition,
( sQ18_spl
<=> relation(sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f388,plain,
( sQ18_spl
| ~ relation(sK7_skl) ),
inference(component_clause,[status(thm)],[f386]) ).
fof(f389,definition,
( sQ19_spl
<=> function(sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f391,plain,
( sQ19_spl
| ~ function(sK7_skl) ),
inference(component_clause,[status(thm)],[f389]) ).
fof(f396,definition,
( sQ21_spl
<=> relation(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f398,plain,
( sQ21_spl
| ~ relation(sK13_skl) ),
inference(component_clause,[status(thm)],[f396]) ).
fof(f399,definition,
( sQ22_spl
<=> function(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( sQ22_spl
| ~ function(sK13_skl) ),
inference(component_clause,[status(thm)],[f399]) ).
fof(f402,definition,
( sQ23_spl
<=> relation_rng(sK13_skl) = relation_dom(function_inverse(sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f403,plain,
( ~ sQ23_spl
| relation_rng(sK13_skl) = relation_dom(function_inverse(sK13_skl)) ),
inference(component_clause,[status(thm)],[f402]) ).
fof(f405,plain,
( sQ23_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f385,f396,f399,f402]) ).
fof(f406,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f401,f134]) ).
fof(f407,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f406]) ).
fof(f408,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f398,f133]) ).
fof(f409,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f408]) ).
fof(f435,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f391,f102]) ).
fof(f436,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f435]) ).
fof(f437,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f388,f101]) ).
fof(f438,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f437]) ).
fof(f450,plain,
! [X0] :
( ~ empty(X0)
| relation_dom(X0) = sK4_skl ),
inference(forward_demodulation,[status(thm)],[f310,f308]) ).
fof(f453,plain,
relation_dom(sK4_skl) = sK4_skl,
inference(resolution,[status(thm)],[f450,f93]) ).
fof(f508,plain,
! [X0,X1] :
( ~ sQ23_spl
| apply(relation_composition(function_inverse(sK13_skl),X0),X1) = apply(X0,apply(function_inverse(sK13_skl),X1))
| ~ in(X1,relation_rng(sK13_skl))
| ~ function(X0)
| ~ relation(X0)
| ~ function(function_inverse(sK13_skl))
| ~ relation(function_inverse(sK13_skl)) ),
inference(paramodulation,[status(thm)],[f403,f111]) ).
fof(f519,definition,
( sQ36_spl
<=> relation(function_inverse(sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f521,plain,
( sQ36_spl
| ~ relation(function_inverse(sK13_skl)) ),
inference(component_clause,[status(thm)],[f519]) ).
fof(f522,definition,
( sQ37_spl
<=> function(function_inverse(sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f524,plain,
( sQ37_spl
| ~ function(function_inverse(sK13_skl)) ),
inference(component_clause,[status(thm)],[f522]) ).
fof(f539,definition,
! [X0,X1] :
( sQ42_spl
<=> ( apply(relation_composition(function_inverse(sK13_skl),X0),X1) = apply(X0,apply(function_inverse(sK13_skl),X1))
| ~ in(X1,relation_rng(sK13_skl))
| ~ function(X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f540,plain,
! [X0,X1] :
( ~ sQ42_spl
| apply(relation_composition(function_inverse(sK13_skl),X0),X1) = apply(X0,apply(function_inverse(sK13_skl),X1))
| ~ in(X1,relation_rng(sK13_skl))
| ~ function(X0)
| ~ relation(X0) ),
inference(component_clause,[status(thm)],[f539]) ).
fof(f542,plain,
( ~ sQ23_spl
| sQ42_spl
| ~ sQ37_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f508,f519,f522,f539,f402]) ).
fof(f552,plain,
( sQ36_spl
| ~ function(sK13_skl)
| ~ relation(sK13_skl) ),
inference(resolution,[status(thm)],[f521,f52]) ).
fof(f553,plain,
( sQ36_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f552,f396,f399,f519]) ).
fof(f554,plain,
( sQ37_spl
| ~ function(sK13_skl)
| ~ relation(sK13_skl) ),
inference(resolution,[status(thm)],[f524,f53]) ).
fof(f555,plain,
( sQ37_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f554,f396,f399,f522]) ).
fof(f625,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)],[f165,f374]) ).
fof(f626,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)],[f625,f53]) ).
fof(f641,definition,
( sQ48_spl
<=> one_to_one(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f643,plain,
( sQ48_spl
| ~ one_to_one(sK13_skl) ),
inference(component_clause,[status(thm)],[f641]) ).
fof(f650,plain,
( sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f643,f135]) ).
fof(f651,plain,
sQ48_spl,
inference(contradiction_clause,[status(thm)],[f650]) ).
fof(f811,definition,
( sQ54_spl
<=> relation_dom(sK4_skl) = relation_rng(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f813,plain,
( sQ54_spl
| relation_dom(sK4_skl) != relation_rng(sK4_skl) ),
inference(component_clause,[status(thm)],[f811]) ).
fof(f822,plain,
( sQ54_spl
| sK4_skl != relation_rng(sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f453,f813]) ).
fof(f823,plain,
( sQ54_spl
| sK4_skl != sK4_skl ),
inference(forward_demodulation,[status(thm)],[f360,f822]) ).
fof(f824,plain,
( sQ54_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f823]) ).
fof(f825,plain,
sQ54_spl,
inference(contradiction_clause,[status(thm)],[f824]) ).
fof(f874,plain,
! [X0] :
( ~ sQ42_spl
| apply(relation_composition(function_inverse(sK13_skl),X0),sK14_skl) = apply(X0,apply(function_inverse(sK13_skl),sK14_skl))
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f540,f136]) ).
fof(f888,plain,
( ~ sQ42_spl
| apply(relation_composition(function_inverse(sK13_skl),sK13_skl),sK14_skl) = apply(sK13_skl,apply(function_inverse(sK13_skl),sK14_skl))
| ~ relation(sK13_skl) ),
inference(resolution,[status(thm)],[f874,f134]) ).
fof(f900,definition,
( sQ62_spl
<=> relation(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f902,plain,
( sQ62_spl
| ~ relation(sK1_skl) ),
inference(component_clause,[status(thm)],[f900]) ).
fof(f919,definition,
( sQ67_spl
<=> apply(relation_composition(function_inverse(sK13_skl),sK13_skl),sK14_skl) = apply(sK13_skl,apply(function_inverse(sK13_skl),sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f920,plain,
( ~ sQ67_spl
| apply(relation_composition(function_inverse(sK13_skl),sK13_skl),sK14_skl) = apply(sK13_skl,apply(function_inverse(sK13_skl),sK14_skl)) ),
inference(component_clause,[status(thm)],[f919]) ).
fof(f922,plain,
( ~ sQ42_spl
| sQ67_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f888,f396,f919,f539]) ).
fof(f923,plain,
( sQ62_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f902,f84]) ).
fof(f924,plain,
sQ62_spl,
inference(contradiction_clause,[status(thm)],[f923]) ).
fof(f1225,plain,
! [X0] :
( ~ function(sK13_skl)
| ~ relation(sK13_skl)
| X0 = apply(sK13_skl,apply(function_inverse(sK13_skl),X0))
| ~ in(X0,relation_rng(sK13_skl)) ),
inference(resolution,[status(thm)],[f626,f135]) ).
fof(f1231,definition,
! [X0] :
( sQ92_spl
<=> ( X0 = apply(sK13_skl,apply(function_inverse(sK13_skl),X0))
| ~ in(X0,relation_rng(sK13_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1232,plain,
! [X0] :
( ~ sQ92_spl
| X0 = apply(sK13_skl,apply(function_inverse(sK13_skl),X0))
| ~ in(X0,relation_rng(sK13_skl)) ),
inference(component_clause,[status(thm)],[f1231]) ).
fof(f1234,plain,
( ~ sQ22_spl
| ~ sQ21_spl
| sQ92_spl ),
inference(split_clause,[status(thm)],[f1225,f1231,f396,f399]) ).
fof(f1239,plain,
( ~ sQ92_spl
| sK14_skl = apply(sK13_skl,apply(function_inverse(sK13_skl),sK14_skl)) ),
inference(resolution,[status(thm)],[f1232,f136]) ).
fof(f1244,plain,
( ~ sQ92_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1239,f155]) ).
fof(f1245,plain,
( ~ sQ92_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1244]) ).
fof(f1246,plain,
( sQ1_spl
| ~ sQ67_spl
| sK14_skl != apply(sK13_skl,apply(function_inverse(sK13_skl),sK14_skl)) ),
inference(forward_demodulation,[status(thm)],[f920,f158]) ).
fof(f1247,plain,
( ~ sQ92_spl
| sQ1_spl
| ~ sQ67_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1239,f1246]) ).
fof(f1248,plain,
( ~ sQ92_spl
| sQ1_spl
| ~ sQ67_spl ),
inference(contradiction_clause,[status(thm)],[f1247]) ).
fof(f1249,plain,
$false,
inference(sat_refutation,[status(thm)],[f159,f405,f407,f409,f436,f438,f542,f553,f555,f651,f825,f922,f924,f1234,f1245,f1248]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU220+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 06:01:28 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.47 % Refutation found
% 0.09/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.49 % Elapsed time: 0.118847 seconds
% 0.09/0.49 % CPU time: 0.686923 seconds
% 0.09/0.49 % Total memory used: 96.246 MB
% 0.09/0.49 % Net memory used: 95.293 MB
%------------------------------------------------------------------------------