%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU023+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:19:06 PM UTC 2026
% Result : Theorem 0.19s 0.53s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 62 ( 9 unt; 9 def)
% Number of atoms : 285 ( 68 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 366 ( 143 ~; 141 |; 57 &)
% ( 12 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 9 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 70 ( 60 !; 10 ?)
% 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(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,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( in(A,relation_dom(B))
& one_to_one(B) )
=> ( A = apply(relation_composition(B,function_inverse(B)),A)
& A = apply(function_inverse(B),apply(B,A)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( in(A,relation_dom(B))
& one_to_one(B) )
=> ( A = apply(relation_composition(B,function_inverse(B)),A)
& A = apply(function_inverse(B),apply(B,A)) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f52,plain,
! [A] :
( ( function(function_inverse(A))
& relation(function_inverse(A)) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f53,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [X0] :
( function(function_inverse(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f120,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(f121,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)],[f120]) ).
fof(f122,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)],[f121]) ).
fof(f132,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(f133,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(f134,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)],[f132,f133]) ).
fof(f135,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)],[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)) )
| ? [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)],[f135]) ).
fof(f137,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))],[f136]) ).
fof(f141,plain,
! [X0,X1,X2,X3] :
( X2 = apply(X1,X3)
| X3 != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| X1 != function_inverse(X0)
| ~ function(X1)
| ~ relation(X1)
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f145,plain,
? [A,B] :
( ( A != apply(relation_composition(B,function_inverse(B)),A)
| A != apply(function_inverse(B),apply(B,A)) )
& in(A,relation_dom(B))
& one_to_one(B)
& function(B)
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f146,plain,
? [B] :
( ? [A] :
( ( A != apply(relation_composition(B,function_inverse(B)),A)
| A != apply(function_inverse(B),apply(B,A)) )
& in(A,relation_dom(B))
& one_to_one(B) )
& function(B)
& relation(B) ),
inference(miniscoping,[status(thm)],[f145]) ).
fof(f147,plain,
( ( sK16_skl != apply(relation_composition(sK15_skl,function_inverse(sK15_skl)),sK16_skl)
| sK16_skl != apply(function_inverse(sK15_skl),apply(sK15_skl,sK16_skl)) )
& in(sK16_skl,relation_dom(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)],[f146]) ).
fof(f148,plain,
relation(sK15_skl),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f149,plain,
function(sK15_skl),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f150,plain,
one_to_one(sK15_skl),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f151,plain,
in(sK16_skl,relation_dom(sK15_skl)),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f152,plain,
( sK16_skl != apply(relation_composition(sK15_skl,function_inverse(sK15_skl)),sK16_skl)
| sK16_skl != apply(function_inverse(sK15_skl),apply(sK15_skl,sK16_skl)) ),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f171,definition,
( sQ0_spl
<=> sK16_skl = apply(function_inverse(sK15_skl),apply(sK15_skl,sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( ~ sQ0_spl
| sK16_skl = apply(function_inverse(sK15_skl),apply(sK15_skl,sK16_skl)) ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f173,plain,
( sQ0_spl
| sK16_skl != apply(function_inverse(sK15_skl),apply(sK15_skl,sK16_skl)) ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,definition,
( sQ1_spl
<=> sK16_skl = apply(relation_composition(sK15_skl,function_inverse(sK15_skl)),sK16_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f177,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f152,f171,f174]) ).
fof(f181,plain,
! [X0,X1] :
( X1 = apply(function_inverse(X0),apply(X0,X1))
| ~ in(X1,relation_dom(X0))
| ~ function(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f141]) ).
fof(f194,definition,
( sQ2_spl
<=> relation(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( sQ2_spl
| ~ relation(sK15_skl) ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f208,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f196,f148]) ).
fof(f209,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f208]) ).
fof(f325,definition,
( sQ23_spl
<=> function(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f327,plain,
( sQ23_spl
| ~ function(sK15_skl) ),
inference(component_clause,[status(thm)],[f325]) ).
fof(f328,definition,
( sQ24_spl
<=> one_to_one(sK15_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f330,plain,
( sQ24_spl
| ~ one_to_one(sK15_skl) ),
inference(component_clause,[status(thm)],[f328]) ).
fof(f338,plain,
! [X0,X1] :
( X1 = apply(function_inverse(X0),apply(X0,X1))
| ~ in(X1,relation_dom(X0))
| ~ function(function_inverse(X0))
| ~ one_to_one(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f181,f53]) ).
fof(f339,plain,
( sQ0_spl
| ~ in(sK16_skl,relation_dom(sK15_skl))
| ~ function(function_inverse(sK15_skl))
| ~ one_to_one(sK15_skl)
| ~ function(sK15_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f338,f173]) ).
fof(f340,definition,
( sQ25_spl
<=> function(function_inverse(sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f342,plain,
( sQ25_spl
| ~ function(function_inverse(sK15_skl)) ),
inference(component_clause,[status(thm)],[f340]) ).
fof(f343,definition,
( sQ26_spl
<=> in(sK16_skl,relation_dom(sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f345,plain,
( sQ26_spl
| ~ in(sK16_skl,relation_dom(sK15_skl)) ),
inference(component_clause,[status(thm)],[f343]) ).
fof(f346,plain,
( sQ0_spl
| ~ sQ26_spl
| ~ sQ25_spl
| ~ sQ24_spl
| ~ sQ23_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f339,f194,f325,f328,f340,f343,f171]) ).
fof(f347,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f345,f151]) ).
fof(f348,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f347]) ).
fof(f349,plain,
( sQ25_spl
| ~ function(sK15_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f342,f54]) ).
fof(f351,plain,
( sQ25_spl
| ~ sQ23_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f349,f194,f325,f340]) ).
fof(f352,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f327,f149]) ).
fof(f353,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f352]) ).
fof(f354,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f330,f150]) ).
fof(f355,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f354]) ).
fof(f478,plain,
( ~ sQ0_spl
| apply(relation_composition(sK15_skl,function_inverse(sK15_skl)),sK16_skl) = sK16_skl
| ~ in(sK16_skl,relation_dom(sK15_skl))
| ~ function(function_inverse(sK15_skl))
| ~ relation(function_inverse(sK15_skl))
| ~ function(sK15_skl)
| ~ relation(sK15_skl) ),
inference(paramodulation,[status(thm)],[f172,f122]) ).
fof(f487,definition,
( sQ48_spl
<=> relation(function_inverse(sK15_skl)) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f489,plain,
( sQ48_spl
| ~ relation(function_inverse(sK15_skl)) ),
inference(component_clause,[status(thm)],[f487]) ).
fof(f490,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ sQ26_spl
| ~ sQ25_spl
| ~ sQ48_spl
| ~ sQ23_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f478,f194,f325,f487,f340,f343,f174,f171]) ).
fof(f516,plain,
( sQ48_spl
| ~ function(sK15_skl)
| ~ relation(sK15_skl) ),
inference(resolution,[status(thm)],[f489,f53]) ).
fof(f518,plain,
( sQ48_spl
| ~ sQ23_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f516,f194,f325,f487]) ).
fof(f519,plain,
$false,
inference(sat_refutation,[status(thm)],[f177,f209,f346,f348,f351,f353,f355,f490,f518]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU023+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n006.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 05:47:27 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.48 % Drodi V4.1.1
% 0.19/0.53 % Refutation found
% 0.19/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.56 % Elapsed time: 0.101683 seconds
% 0.19/0.56 % CPU time: 0.323961 seconds
% 0.19/0.56 % Total memory used: 52.718 MB
% 0.19/0.56 % Net memory used: 52.412 MB
%------------------------------------------------------------------------------