%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU215+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 : 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 02:19:43 PM UTC 2026
% Result : Theorem 0.19s 0.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of formulae : 80 ( 12 unt; 11 def)
% Number of atoms : 299 ( 38 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 357 ( 138 ~; 142 |; 44 &)
% ( 17 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 73 ( 67 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) )
& ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(relation_composition(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( ( function(B)
& relation(B)
& function(A)
& relation(A) )
=> ( function(relation_composition(A,B))
& relation(relation_composition(A,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
<=> ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
=> apply(relation_composition(C,B),A) = apply(B,apply(C,A)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [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(f37,negated_conjecture,
~ ! [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)) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f49,plain,
! [A] :
( ! [B,C] :
( ( ( C = apply(A,B)
<=> C = empty_set )
| in(B,relation_dom(A)) )
& ( ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f50,plain,
! [A] :
( ! [B,C] :
( ( ( ( C != empty_set
| C = apply(A,B) )
& ( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ( ( ( ~ in(ordered_pair(B,C),A)
| C = apply(A,B) )
& ( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [A] :
( ( ! [B] :
( ( ! [C] :
( C != empty_set
| C = apply(A,B) )
& ! [C] :
( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ! [B] :
( ( ! [C] :
( ~ in(ordered_pair(B,C),A)
| C = apply(A,B) )
& ! [C] :
( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f50]) ).
fof(f54,plain,
! [X0,X1,X2] :
( X2 = empty_set
| X2 != apply(X0,X1)
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f57,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f58,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f67,plain,
! [A,B] :
( ( function(relation_composition(A,B))
& relation(relation_composition(A,B)) )
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f69,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f102,plain,
! [A,B] :
( ! [C] :
( ( in(A,relation_dom(relation_composition(C,B)))
<=> ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f103,plain,
! [A,B] :
( ! [C] :
( ( ( ~ in(apply(C,A),relation_dom(B))
| ~ in(A,relation_dom(C))
| in(A,relation_dom(relation_composition(C,B))) )
& ( ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) )
| ~ in(A,relation_dom(relation_composition(C,B))) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ~ in(apply(C,A),relation_dom(B))
| ~ in(A,relation_dom(C))
| in(A,relation_dom(relation_composition(C,B))) )
& ! [A] :
( ( in(apply(C,A),relation_dom(B))
& in(A,relation_dom(C)) )
| ~ in(A,relation_dom(relation_composition(C,B))) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f103]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ~ in(apply(X1,X2),relation_dom(X0))
| ~ in(X2,relation_dom(X1))
| in(X2,relation_dom(relation_composition(X1,X0)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f108,plain,
! [A,B] :
( ! [C] :
( apply(relation_composition(C,B),A) = apply(B,apply(C,A))
| ~ in(A,relation_dom(relation_composition(C,B)))
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f109,plain,
! [B] :
( ! [C] :
( ! [A] :
( apply(relation_composition(C,B),A) = apply(B,apply(C,A))
| ~ in(A,relation_dom(relation_composition(C,B))) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f108]) ).
fof(f110,plain,
! [X0,X1,X2] :
( apply(relation_composition(X1,X0),X2) = apply(X0,apply(X1,X2))
| ~ in(X2,relation_dom(relation_composition(X1,X0)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f111,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)],[f37]) ).
fof(f112,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)],[f111]) ).
fof(f113,plain,
( apply(relation_composition(sK7_skl,sK8_skl),sK9_skl) != apply(sK8_skl,apply(sK7_skl,sK9_skl))
& in(sK9_skl,relation_dom(sK7_skl))
& function(sK8_skl)
& relation(sK8_skl)
& function(sK7_skl)
& relation(sK7_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl,sK9_skl]),skolemize(B,sK7_skl),skolemize(C,sK8_skl),skolemize(A,sK9_skl)],[f112]) ).
fof(f114,plain,
relation(sK7_skl),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
function(sK7_skl),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f116,plain,
relation(sK8_skl),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f117,plain,
function(sK8_skl),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f118,plain,
in(sK9_skl,relation_dom(sK7_skl)),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f119,plain,
apply(relation_composition(sK7_skl,sK8_skl),sK9_skl) != apply(sK8_skl,apply(sK7_skl,sK9_skl)),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f131,plain,
! [X0,X1] :
( apply(X0,X1) = empty_set
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f54]) ).
fof(f167,definition,
( sQ2_spl
<=> relation(sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f169,plain,
( sQ2_spl
| ~ relation(sK7_skl) ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f181,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f169,f114]) ).
fof(f182,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f181]) ).
fof(f206,definition,
( sQ7_spl
<=> function(sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f208,plain,
( sQ7_spl
| ~ function(sK7_skl) ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f259,plain,
( ~ in(sK9_skl,relation_dom(relation_composition(sK7_skl,sK8_skl)))
| ~ function(sK7_skl)
| ~ relation(sK7_skl)
| ~ function(sK8_skl)
| ~ relation(sK8_skl) ),
inference(resolution,[status(thm)],[f110,f119]) ).
fof(f260,definition,
( sQ8_spl
<=> relation(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f262,plain,
( sQ8_spl
| ~ relation(sK8_skl) ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f263,definition,
( sQ9_spl
<=> function(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f265,plain,
( sQ9_spl
| ~ function(sK8_skl) ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f266,definition,
( sQ10_spl
<=> in(sK9_skl,relation_dom(relation_composition(sK7_skl,sK8_skl))) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f268,plain,
( sQ10_spl
| ~ in(sK9_skl,relation_dom(relation_composition(sK7_skl,sK8_skl))) ),
inference(component_clause,[status(thm)],[f266]) ).
fof(f269,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f259,f260,f263,f167,f206,f266]) ).
fof(f270,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f208,f115]) ).
fof(f271,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f270]) ).
fof(f272,plain,
( sQ10_spl
| ~ in(apply(sK7_skl,sK9_skl),relation_dom(sK8_skl))
| ~ in(sK9_skl,relation_dom(sK7_skl))
| ~ function(sK7_skl)
| ~ relation(sK7_skl)
| ~ function(sK8_skl)
| ~ relation(sK8_skl) ),
inference(resolution,[status(thm)],[f268,f107]) ).
fof(f274,plain,
( sQ10_spl
| apply(relation_composition(sK7_skl,sK8_skl),sK9_skl) = empty_set
| ~ function(relation_composition(sK7_skl,sK8_skl))
| ~ relation(relation_composition(sK7_skl,sK8_skl)) ),
inference(resolution,[status(thm)],[f268,f131]) ).
fof(f276,definition,
( sQ11_spl
<=> in(sK9_skl,relation_dom(sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f278,plain,
( sQ11_spl
| ~ in(sK9_skl,relation_dom(sK7_skl)) ),
inference(component_clause,[status(thm)],[f276]) ).
fof(f279,definition,
( sQ12_spl
<=> in(apply(sK7_skl,sK9_skl),relation_dom(sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f281,plain,
( sQ12_spl
| ~ in(apply(sK7_skl,sK9_skl),relation_dom(sK8_skl)) ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f282,plain,
( sQ10_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f272,f260,f263,f167,f206,f276,f279,f266]) ).
fof(f286,definition,
( sQ14_spl
<=> relation(relation_composition(sK7_skl,sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f288,plain,
( sQ14_spl
| ~ relation(relation_composition(sK7_skl,sK8_skl)) ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f289,definition,
( sQ15_spl
<=> function(relation_composition(sK7_skl,sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f291,plain,
( sQ15_spl
| ~ function(relation_composition(sK7_skl,sK8_skl)) ),
inference(component_clause,[status(thm)],[f289]) ).
fof(f293,definition,
( sQ16_spl
<=> apply(relation_composition(sK7_skl,sK8_skl),sK9_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f294,plain,
( ~ sQ16_spl
| apply(relation_composition(sK7_skl,sK8_skl),sK9_skl) = empty_set ),
inference(component_clause,[status(thm)],[f293]) ).
fof(f296,plain,
( sQ10_spl
| sQ16_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f274,f286,f289,f293,f266]) ).
fof(f304,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f265,f117]) ).
fof(f305,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f304]) ).
fof(f306,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f262,f116]) ).
fof(f307,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f306]) ).
fof(f308,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f278,f118]) ).
fof(f309,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f308]) ).
fof(f318,plain,
( sQ15_spl
| ~ function(sK8_skl)
| ~ relation(sK8_skl)
| ~ function(sK7_skl)
| ~ relation(sK7_skl) ),
inference(resolution,[status(thm)],[f291,f69]) ).
fof(f320,plain,
( sQ15_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f318,f167,f206,f260,f263,f289]) ).
fof(f323,plain,
( sQ12_spl
| apply(sK8_skl,apply(sK7_skl,sK9_skl)) = empty_set
| ~ function(sK8_skl)
| ~ relation(sK8_skl) ),
inference(resolution,[status(thm)],[f281,f131]) ).
fof(f330,definition,
( sQ20_spl
<=> apply(sK8_skl,apply(sK7_skl,sK9_skl)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f331,plain,
( ~ sQ20_spl
| apply(sK8_skl,apply(sK7_skl,sK9_skl)) = empty_set ),
inference(component_clause,[status(thm)],[f330]) ).
fof(f333,plain,
( sQ12_spl
| sQ20_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f323,f260,f263,f330,f279]) ).
fof(f341,plain,
( ~ sQ20_spl
| apply(relation_composition(sK7_skl,sK8_skl),sK9_skl) != empty_set ),
inference(backward_demodulation,[status(thm)],[f331,f119]) ).
fof(f356,plain,
( sQ14_spl
| ~ relation(sK8_skl)
| ~ relation(sK7_skl) ),
inference(resolution,[status(thm)],[f288,f58]) ).
fof(f363,plain,
( sQ14_spl
| ~ sQ8_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f356,f167,f260,f286]) ).
fof(f364,plain,
( ~ sQ16_spl
| ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f294,f341]) ).
fof(f365,plain,
( ~ sQ16_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f364]) ).
fof(f366,plain,
$false,
inference(sat_refutation,[status(thm)],[f182,f269,f271,f282,f296,f305,f307,f309,f320,f333,f363,f365]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU215+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n002.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 06:01:32 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.49 % Drodi V4.1.1
% 0.19/0.52 % Refutation found
% 0.19/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.57 % Elapsed time: 0.105801 seconds
% 0.19/0.57 % CPU time: 0.191313 seconds
% 0.19/0.57 % Total memory used: 30.311 MB
% 0.19/0.57 % Net memory used: 30.137 MB
%------------------------------------------------------------------------------