%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU225+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 : n007.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 0.23s 0.58s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 72 ( 8 unt; 7 def)
% Number of atoms : 296 ( 62 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 372 ( 148 ~; 152 |; 44 &)
% ( 15 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 113 ( 105 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,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(f16,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A,B] :
( ( function(A)
& relation(A) )
=> ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,A)
& in(B,relation_dom(C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,A)
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,A)
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f61,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)],[f7]) ).
fof(f62,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)],[f61]) ).
fof(f63,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)],[f62]) ).
fof(f66,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)],[f63]) ).
fof(f69,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f70,plain,
! [A] :
( ! [B] : relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f87,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)],[f26]) ).
fof(f88,plain,
! [A] :
( ( ! [B] : function(relation_dom_restriction(A,B))
& ! [B] : relation(relation_dom_restriction(A,B)) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f87]) ).
fof(f90,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f100,plain,
! [A,B,C] :
( ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,A)
& in(B,relation_dom(C)) ) )
| ~ function(C)
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f101,plain,
! [A,B,C] :
( ( ( ~ in(B,A)
| ~ in(B,relation_dom(C))
| in(B,relation_dom(relation_dom_restriction(C,A))) )
& ( ( in(B,A)
& in(B,relation_dom(C)) )
| ~ in(B,relation_dom(relation_dom_restriction(C,A))) ) )
| ~ function(C)
| ~ relation(C) ),
inference(NNF_transformation,[status(thm)],[f100]) ).
fof(f102,plain,
! [C] :
( ( ! [A,B] :
( ~ in(B,A)
| ~ in(B,relation_dom(C))
| in(B,relation_dom(relation_dom_restriction(C,A))) )
& ! [A,B] :
( ( in(B,A)
& in(B,relation_dom(C)) )
| ~ in(B,relation_dom(relation_dom_restriction(C,A))) ) )
| ~ function(C)
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f101]) ).
fof(f103,plain,
! [X0,X1,X2] :
( in(X1,relation_dom(X0))
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X1,relation_dom(X0))
| in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f135,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)],[f43]) ).
fof(f136,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)],[f135]) ).
fof(f137,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)],[f136]) ).
fof(f138,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ( apply(B,sK9_skl(A,C,B)) != apply(C,sK9_skl(A,C,B))
& in(sK9_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,[sK9_skl]),skolemize(D,sK9_skl(A,C,B))],[f137]) ).
fof(f140,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)],[f138]) ).
fof(f145,plain,
? [A,B,C] :
( apply(relation_dom_restriction(C,A),B) != apply(C,B)
& in(B,A)
& function(C)
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f146,plain,
? [C] :
( ? [A,B] :
( apply(relation_dom_restriction(C,A),B) != apply(C,B)
& in(B,A) )
& function(C)
& relation(C) ),
inference(miniscoping,[status(thm)],[f145]) ).
fof(f147,plain,
( apply(relation_dom_restriction(sK10_skl,sK11_skl),sK12_skl) != apply(sK10_skl,sK12_skl)
& in(sK12_skl,sK11_skl)
& function(sK10_skl)
& relation(sK10_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl]),skolemize(C,sK10_skl),skolemize(A,sK11_skl),skolemize(B,sK12_skl)],[f146]) ).
fof(f148,plain,
relation(sK10_skl),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f149,plain,
function(sK10_skl),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f150,plain,
in(sK12_skl,sK11_skl),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f151,plain,
apply(relation_dom_restriction(sK10_skl,sK11_skl),sK12_skl) != apply(sK10_skl,sK12_skl),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f159,plain,
! [X0,X1] :
( apply(X0,X1) = empty_set
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f66]) ).
fof(f162,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)],[f140]) ).
fof(f170,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X0,X2),X1) = empty_set
| ~ function(relation_dom_restriction(X0,X2))
| ~ relation(relation_dom_restriction(X0,X2))
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f103,f159]) ).
fof(f171,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X0,X2),X1) = empty_set
| ~ function(relation_dom_restriction(X0,X2))
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f71]) ).
fof(f218,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)],[f162,f71]) ).
fof(f219,plain,
( ~ in(sK12_skl,relation_dom(relation_dom_restriction(sK10_skl,sK11_skl)))
| ~ function(sK10_skl)
| ~ relation(sK10_skl)
| ~ function(relation_dom_restriction(sK10_skl,sK11_skl)) ),
inference(resolution,[status(thm)],[f218,f151]) ).
fof(f220,definition,
( sQ8_spl
<=> function(relation_dom_restriction(sK10_skl,sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f222,plain,
( sQ8_spl
| ~ function(relation_dom_restriction(sK10_skl,sK11_skl)) ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,definition,
( sQ9_spl
<=> relation(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( sQ9_spl
| ~ relation(sK10_skl) ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,definition,
( sQ10_spl
<=> function(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f228,plain,
( sQ10_spl
| ~ function(sK10_skl) ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f229,definition,
( sQ11_spl
<=> in(sK12_skl,relation_dom(relation_dom_restriction(sK10_skl,sK11_skl))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f231,plain,
( sQ11_spl
| ~ in(sK12_skl,relation_dom(relation_dom_restriction(sK10_skl,sK11_skl))) ),
inference(component_clause,[status(thm)],[f229]) ).
fof(f232,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f219,f220,f223,f226,f229]) ).
fof(f233,plain,
( sQ11_spl
| ~ in(sK12_skl,sK11_skl)
| ~ in(sK12_skl,relation_dom(sK10_skl))
| ~ function(sK10_skl)
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f231,f105]) ).
fof(f235,definition,
( sQ12_spl
<=> in(sK12_skl,relation_dom(sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f237,plain,
( sQ12_spl
| ~ in(sK12_skl,relation_dom(sK10_skl)) ),
inference(component_clause,[status(thm)],[f235]) ).
fof(f238,definition,
( sQ13_spl
<=> in(sK12_skl,sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f240,plain,
( sQ13_spl
| ~ in(sK12_skl,sK11_skl) ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,plain,
( sQ11_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f233,f223,f226,f235,f238,f229]) ).
fof(f249,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f228,f149]) ).
fof(f250,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f249]) ).
fof(f251,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f225,f148]) ).
fof(f252,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f251]) ).
fof(f253,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f240,f150]) ).
fof(f254,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f253]) ).
fof(f255,plain,
( sQ8_spl
| ~ function(sK10_skl)
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f222,f90]) ).
fof(f257,plain,
( sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f255,f223,f226,f220]) ).
fof(f258,plain,
( sQ12_spl
| apply(sK10_skl,sK12_skl) = empty_set
| ~ function(sK10_skl)
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f237,f159]) ).
fof(f259,definition,
( sQ16_spl
<=> apply(sK10_skl,sK12_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f260,plain,
( ~ sQ16_spl
| apply(sK10_skl,sK12_skl) = empty_set ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f262,plain,
( sQ12_spl
| sQ16_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f258,f223,f226,f259,f235]) ).
fof(f263,plain,
( ~ sQ16_spl
| apply(relation_dom_restriction(sK10_skl,sK11_skl),sK12_skl) != empty_set ),
inference(backward_demodulation,[status(thm)],[f260,f151]) ).
fof(f294,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X0,X2),X1) = empty_set
| in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f171,f90]) ).
fof(f295,plain,
( ~ sQ16_spl
| in(sK12_skl,relation_dom(sK10_skl))
| ~ function(sK10_skl)
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f294,f263]) ).
fof(f296,plain,
( ~ sQ16_spl
| sQ12_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f295,f223,f226,f235,f259]) ).
fof(f297,plain,
$false,
inference(sat_refutation,[status(thm)],[f232,f241,f250,f252,f254,f257,f262,f296]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU225+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n007.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 05:58:35 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.47 % Drodi V4.1.1
% 0.23/0.58 % Refutation found
% 0.23/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.63 % Elapsed time: 0.159303 seconds
% 0.23/0.63 % CPU time: 0.746851 seconds
% 0.23/0.63 % Total memory used: 109.211 MB
% 0.23/0.63 % Net memory used: 108.396 MB
%------------------------------------------------------------------------------