%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU223+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 : n009.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 02:19:46 PM UTC 2026
% Result : Theorem 0.19s 0.50s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 8 unt; 4 def)
% Number of atoms : 157 ( 34 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 187 ( 74 ~; 70 |; 28 &)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 63 ( 55 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f30,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A,B] :
( ( function(A)
& relation(A) )
=> ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f98,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f99,plain,
! [A] :
( ! [B] : relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f98]) ).
fof(f100,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f104,plain,
! [A,B] :
( ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f105,plain,
! [A] :
( ( ! [B] : function(relation_dom_restriction(A,B))
& ! [B] : relation(relation_dom_restriction(A,B)) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f104]) ).
fof(f107,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f115,plain,
? [A,B,C] :
( apply(relation_dom_restriction(C,A),B) != apply(C,B)
& in(B,relation_dom(relation_dom_restriction(C,A)))
& function(C)
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f116,plain,
? [C] :
( ? [A,B] :
( apply(relation_dom_restriction(C,A),B) != apply(C,B)
& in(B,relation_dom(relation_dom_restriction(C,A))) )
& function(C)
& relation(C) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f117,plain,
( apply(relation_dom_restriction(sK9_skl,sK10_skl),sK11_skl) != apply(sK9_skl,sK11_skl)
& in(sK11_skl,relation_dom(relation_dom_restriction(sK9_skl,sK10_skl)))
& function(sK9_skl)
& relation(sK9_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl,sK11_skl]),skolemize(C,sK9_skl),skolemize(A,sK10_skl),skolemize(B,sK11_skl)],[f116]) ).
fof(f118,plain,
relation(sK9_skl),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f119,plain,
function(sK9_skl),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f120,plain,
in(sK11_skl,relation_dom(relation_dom_restriction(sK9_skl,sK10_skl))),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f121,plain,
apply(relation_dom_restriction(sK9_skl,sK10_skl),sK11_skl) != apply(sK9_skl,sK11_skl),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f122,plain,
! [A,B] :
( ! [C] :
( ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f123,plain,
! [A,B] :
( ! [C] :
( ( ( ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A)
| B = relation_dom_restriction(C,A) )
& ( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f122]) ).
fof(f124,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A)
| B = relation_dom_restriction(C,A) )
& ! [A] :
( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f123]) ).
fof(f125,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ( apply(B,sK12_skl(A,C,B)) != apply(C,sK12_skl(A,C,B))
& in(sK12_skl(A,C,B),relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A)
| B = relation_dom_restriction(C,A) )
& ! [A] :
( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl]),skolemize(D,sK12_skl(A,C,B))],[f124]) ).
fof(f127,plain,
! [X0,X1,X2,X3] :
( apply(X0,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X0))
| X0 != relation_dom_restriction(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f131,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X0,X1),X2) = apply(X0,X2)
| ~ in(X2,relation_dom(relation_dom_restriction(X0,X1)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f127]) ).
fof(f137,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X0,X1),X2) = apply(X0,X2)
| ~ in(X2,relation_dom(relation_dom_restriction(X0,X1)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f131,f100]) ).
fof(f138,plain,
( ~ in(sK11_skl,relation_dom(relation_dom_restriction(sK9_skl,sK10_skl)))
| ~ function(sK9_skl)
| ~ relation(sK9_skl)
| ~ function(relation_dom_restriction(sK9_skl,sK10_skl)) ),
inference(resolution,[status(thm)],[f137,f121]) ).
fof(f139,definition,
( sQ0_spl
<=> function(relation_dom_restriction(sK9_skl,sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f141,plain,
( sQ0_spl
| ~ function(relation_dom_restriction(sK9_skl,sK10_skl)) ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
( sQ1_spl
<=> relation(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f144,plain,
( sQ1_spl
| ~ relation(sK9_skl) ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,definition,
( sQ2_spl
<=> function(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f147,plain,
( sQ2_spl
| ~ function(sK9_skl) ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,definition,
( sQ3_spl
<=> in(sK11_skl,relation_dom(relation_dom_restriction(sK9_skl,sK10_skl))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( sQ3_spl
| ~ in(sK11_skl,relation_dom(relation_dom_restriction(sK9_skl,sK10_skl))) ),
inference(component_clause,[status(thm)],[f148]) ).
fof(f151,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f138,f139,f142,f145,f148]) ).
fof(f152,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f150,f120]) ).
fof(f153,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f152]) ).
fof(f154,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f147,f119]) ).
fof(f155,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f154]) ).
fof(f159,plain,
( sQ0_spl
| ~ function(sK9_skl)
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f141,f107]) ).
fof(f160,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f159,f142,f145,f139]) ).
fof(f161,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f144,f118]) ).
fof(f162,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f161]) ).
fof(f163,plain,
$false,
inference(sat_refutation,[status(thm)],[f151,f153,f155,f160,f162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU223+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n009.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 05:59:42 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.47 % Drodi V4.1.1
% 0.19/0.50 % Refutation found
% 0.19/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.55 % Elapsed time: 0.082656 seconds
% 0.24/0.55 % CPU time: 0.101562 seconds
% 0.24/0.55 % Total memory used: 3.247 MB
% 0.24/0.55 % Net memory used: 3.246 MB
%------------------------------------------------------------------------------