%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU221+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 94 ( 9 unt; 14 def)
% Number of atoms : 392 ( 84 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 500 ( 202 ~; 204 |; 61 &)
% ( 19 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 14 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-2 aty)
% Number of variables : 75 ( 66 !; 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/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( function(function_inverse(A))
& relation(function_inverse(A)) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f36,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/sandbox/benchmark/theBenchmark.p') ).
fof(f38,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> one_to_one(function_inverse(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( one_to_one(A)
=> one_to_one(function_inverse(A)) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f53,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(f54,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)],[f53]) ).
fof(f55,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))],[f54]) ).
fof(f57,plain,
! [X0] :
( in(sK0_skl(X0),relation_dom(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f58,plain,
! [X0] :
( in(sK1_skl(X0),relation_dom(X0))
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f59,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)],[f55]) ).
fof(f60,plain,
! [X0] :
( sK0_skl(X0) != sK1_skl(X0)
| one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f61,plain,
! [A] :
( ( function(function_inverse(A))
& relation(function_inverse(A)) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f62,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f138,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(f139,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(f140,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)],[f138,f139]) ).
fof(f141,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)],[f140]) ).
fof(f142,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)],[f141]) ).
fof(f143,plain,
! [A] :
( ! [B] :
( ( ( ( ( sK16_skl(B,A) != apply(B,sK15_skl(B,A))
| ~ in(sK15_skl(B,A),relation_rng(A)) )
& sK15_skl(B,A) = apply(A,sK16_skl(B,A))
& in(sK16_skl(B,A),relation_dom(A)) )
| ~ sP0_prd(sK14_skl(B,A),sK13_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,[sK13_skl,sK14_skl,sK15_skl,sK16_skl]),skolemize(C,sK13_skl(B,A)),skolemize(D,sK14_skl(B,A)),skolemize(C,sK15_skl(B,A)),skolemize(D,sK16_skl(B,A))],[f142]) ).
fof(f144,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)],[f143]) ).
fof(f151,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)],[f36]) ).
fof(f152,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)],[f151]) ).
fof(f153,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)],[f152]) ).
fof(f158,plain,
? [A] :
( ~ one_to_one(function_inverse(A))
& one_to_one(A)
& function(A)
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f159,plain,
( ~ one_to_one(function_inverse(sK17_skl))
& one_to_one(sK17_skl)
& function(sK17_skl)
& relation(sK17_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl]),skolemize(A,sK17_skl)],[f158]) ).
fof(f160,plain,
relation(sK17_skl),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f161,plain,
function(sK17_skl),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f162,plain,
one_to_one(sK17_skl),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f163,plain,
~ one_to_one(function_inverse(sK17_skl)),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f179,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)],[f144]) ).
fof(f187,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)],[f179,f62]) ).
fof(f188,plain,
( relation_dom(function_inverse(sK17_skl)) = relation_rng(sK17_skl)
| ~ function(function_inverse(sK17_skl))
| ~ function(sK17_skl)
| ~ relation(sK17_skl) ),
inference(resolution,[status(thm)],[f187,f162]) ).
fof(f189,definition,
( sQ0_spl
<=> relation(sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( sQ0_spl
| ~ relation(sK17_skl) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,definition,
( sQ1_spl
<=> function(sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( sQ1_spl
| ~ function(sK17_skl) ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,definition,
( sQ2_spl
<=> function(function_inverse(sK17_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f197,plain,
( sQ2_spl
| ~ function(function_inverse(sK17_skl)) ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f198,definition,
( sQ3_spl
<=> relation_dom(function_inverse(sK17_skl)) = relation_rng(sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f199,plain,
( ~ sQ3_spl
| relation_dom(function_inverse(sK17_skl)) = relation_rng(sK17_skl) ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f201,plain,
( sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f188,f189,f192,f195,f198]) ).
fof(f224,definition,
( sQ8_spl
<=> relation(function_inverse(sK17_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f226,plain,
( sQ8_spl
| ~ relation(function_inverse(sK17_skl)) ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f227,definition,
( sQ9_spl
<=> one_to_one(function_inverse(sK17_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f228,plain,
( ~ sQ9_spl
| one_to_one(function_inverse(sK17_skl)) ),
inference(component_clause,[status(thm)],[f227]) ).
fof(f241,plain,
( sQ2_spl
| ~ function(sK17_skl)
| ~ relation(sK17_skl) ),
inference(resolution,[status(thm)],[f197,f63]) ).
fof(f243,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f241,f189,f192,f195]) ).
fof(f244,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f194,f161]) ).
fof(f245,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f244]) ).
fof(f246,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f160]) ).
fof(f247,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f246]) ).
fof(f285,plain,
( in(sK0_skl(function_inverse(sK17_skl)),relation_dom(function_inverse(sK17_skl)))
| ~ function(function_inverse(sK17_skl))
| ~ relation(function_inverse(sK17_skl)) ),
inference(resolution,[status(thm)],[f57,f163]) ).
fof(f287,definition,
( sQ19_spl
<=> in(sK0_skl(function_inverse(sK17_skl)),relation_dom(function_inverse(sK17_skl))) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f288,plain,
( ~ sQ19_spl
| in(sK0_skl(function_inverse(sK17_skl)),relation_dom(function_inverse(sK17_skl))) ),
inference(component_clause,[status(thm)],[f287]) ).
fof(f290,plain,
( sQ19_spl
| ~ sQ2_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f285,f224,f195,f287]) ).
fof(f293,plain,
( ~ sQ19_spl
| ~ sQ3_spl
| in(sK0_skl(function_inverse(sK17_skl)),relation_rng(sK17_skl)) ),
inference(forward_demodulation,[status(thm)],[f199,f288]) ).
fof(f294,plain,
( in(sK1_skl(function_inverse(sK17_skl)),relation_dom(function_inverse(sK17_skl)))
| ~ function(function_inverse(sK17_skl))
| ~ relation(function_inverse(sK17_skl)) ),
inference(resolution,[status(thm)],[f58,f163]) ).
fof(f296,definition,
( sQ20_spl
<=> in(sK1_skl(function_inverse(sK17_skl)),relation_dom(function_inverse(sK17_skl))) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f297,plain,
( ~ sQ20_spl
| in(sK1_skl(function_inverse(sK17_skl)),relation_dom(function_inverse(sK17_skl))) ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f299,plain,
( sQ20_spl
| ~ sQ2_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f294,f224,f195,f296]) ).
fof(f302,plain,
( ~ sQ20_spl
| ~ sQ3_spl
| in(sK1_skl(function_inverse(sK17_skl)),relation_rng(sK17_skl)) ),
inference(forward_demodulation,[status(thm)],[f199,f297]) ).
fof(f303,plain,
( apply(function_inverse(sK17_skl),sK0_skl(function_inverse(sK17_skl))) = apply(function_inverse(sK17_skl),sK1_skl(function_inverse(sK17_skl)))
| ~ function(function_inverse(sK17_skl))
| ~ relation(function_inverse(sK17_skl)) ),
inference(resolution,[status(thm)],[f59,f163]) ).
fof(f305,definition,
( sQ21_spl
<=> apply(function_inverse(sK17_skl),sK0_skl(function_inverse(sK17_skl))) = apply(function_inverse(sK17_skl),sK1_skl(function_inverse(sK17_skl))) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f306,plain,
( ~ sQ21_spl
| apply(function_inverse(sK17_skl),sK0_skl(function_inverse(sK17_skl))) = apply(function_inverse(sK17_skl),sK1_skl(function_inverse(sK17_skl))) ),
inference(component_clause,[status(thm)],[f305]) ).
fof(f308,plain,
( sQ21_spl
| ~ sQ2_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f303,f224,f195,f305]) ).
fof(f311,plain,
( sQ8_spl
| ~ function(sK17_skl)
| ~ relation(sK17_skl) ),
inference(resolution,[status(thm)],[f226,f62]) ).
fof(f313,plain,
( sQ8_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f311,f189,f192,f224]) ).
fof(f317,plain,
( ~ sQ19_spl
| ~ sQ3_spl
| sK0_skl(function_inverse(sK17_skl)) = apply(sK17_skl,apply(function_inverse(sK17_skl),sK0_skl(function_inverse(sK17_skl))))
| ~ one_to_one(sK17_skl)
| ~ function(sK17_skl)
| ~ relation(sK17_skl) ),
inference(resolution,[status(thm)],[f293,f153]) ).
fof(f319,definition,
( sQ22_spl
<=> one_to_one(sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f321,plain,
( sQ22_spl
| ~ one_to_one(sK17_skl) ),
inference(component_clause,[status(thm)],[f319]) ).
fof(f322,definition,
( sQ23_spl
<=> sK0_skl(function_inverse(sK17_skl)) = apply(sK17_skl,apply(function_inverse(sK17_skl),sK0_skl(function_inverse(sK17_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f323,plain,
( ~ sQ23_spl
| sK0_skl(function_inverse(sK17_skl)) = apply(sK17_skl,apply(function_inverse(sK17_skl),sK0_skl(function_inverse(sK17_skl)))) ),
inference(component_clause,[status(thm)],[f322]) ).
fof(f325,plain,
( ~ sQ19_spl
| ~ sQ3_spl
| sQ23_spl
| ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f317,f189,f192,f319,f322,f198,f287]) ).
fof(f326,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f321,f162]) ).
fof(f327,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f326]) ).
fof(f405,plain,
( ~ sQ20_spl
| ~ sQ3_spl
| sK1_skl(function_inverse(sK17_skl)) = apply(sK17_skl,apply(function_inverse(sK17_skl),sK1_skl(function_inverse(sK17_skl))))
| ~ one_to_one(sK17_skl)
| ~ function(sK17_skl)
| ~ relation(sK17_skl) ),
inference(resolution,[status(thm)],[f302,f153]) ).
fof(f407,definition,
( sQ39_spl
<=> sK1_skl(function_inverse(sK17_skl)) = apply(sK17_skl,apply(function_inverse(sK17_skl),sK1_skl(function_inverse(sK17_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f408,plain,
( ~ sQ39_spl
| sK1_skl(function_inverse(sK17_skl)) = apply(sK17_skl,apply(function_inverse(sK17_skl),sK1_skl(function_inverse(sK17_skl)))) ),
inference(component_clause,[status(thm)],[f407]) ).
fof(f410,plain,
( ~ sQ20_spl
| ~ sQ3_spl
| sQ39_spl
| ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f405,f189,f192,f319,f407,f198,f296]) ).
fof(f415,definition,
( sQ40_spl
<=> sK0_skl(function_inverse(sK17_skl)) = sK1_skl(function_inverse(sK17_skl)) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f416,plain,
( ~ sQ40_spl
| sK0_skl(function_inverse(sK17_skl)) = sK1_skl(function_inverse(sK17_skl)) ),
inference(component_clause,[status(thm)],[f415]) ).
fof(f417,plain,
( sQ40_spl
| sK0_skl(function_inverse(sK17_skl)) != sK1_skl(function_inverse(sK17_skl)) ),
inference(component_clause,[status(thm)],[f415]) ).
fof(f505,plain,
( ~ sQ40_spl
| one_to_one(function_inverse(sK17_skl))
| ~ function(function_inverse(sK17_skl))
| ~ relation(function_inverse(sK17_skl)) ),
inference(resolution,[status(thm)],[f416,f60]) ).
fof(f509,plain,
( ~ sQ40_spl
| sQ9_spl
| ~ sQ2_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f505,f224,f195,f227,f415]) ).
fof(f849,plain,
( ~ sQ39_spl
| ~ sQ21_spl
| sK1_skl(function_inverse(sK17_skl)) = apply(sK17_skl,apply(function_inverse(sK17_skl),sK0_skl(function_inverse(sK17_skl)))) ),
inference(forward_demodulation,[status(thm)],[f306,f408]) ).
fof(f850,plain,
( ~ sQ39_spl
| ~ sQ21_spl
| ~ sQ23_spl
| sK1_skl(function_inverse(sK17_skl)) = sK0_skl(function_inverse(sK17_skl)) ),
inference(forward_demodulation,[status(thm)],[f323,f849]) ).
fof(f851,plain,
( ~ sQ39_spl
| ~ sQ21_spl
| ~ sQ23_spl
| sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f850,f417]) ).
fof(f852,plain,
( ~ sQ39_spl
| ~ sQ21_spl
| ~ sQ23_spl
| sQ40_spl ),
inference(contradiction_clause,[status(thm)],[f851]) ).
fof(f853,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f228,f163]) ).
fof(f854,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f853]) ).
fof(f855,plain,
$false,
inference(sat_refutation,[status(thm)],[f201,f243,f245,f247,f290,f299,f308,f313,f325,f327,f410,f509,f852,f854]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU221+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.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 06:02:35 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
% 0.13/0.44 % Elapsed time: 0.063033 seconds
% 0.13/0.44 % CPU time: 0.202465 seconds
% 0.13/0.44 % Total memory used: 84.547 MB
% 0.13/0.44 % Net memory used: 84.357 MB
%------------------------------------------------------------------------------