%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU003+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 : 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 02:19:04 PM UTC 2026
% Result : Theorem 0.15s 0.54s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 28
% Syntax : Number of formulae : 142 ( 34 unt; 15 def)
% Number of atoms : 395 ( 45 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 415 ( 162 ~; 157 |; 59 &)
% ( 23 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 16 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 129 ( 113 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
? [A] :
( function(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,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(f30,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( relation_dom(relation_composition(B,A)) = relation_dom(B)
=> subset(relation_rng(B),relation_dom(A)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( relation_dom(relation_composition(B,A)) = relation_dom(B)
=> subset(relation_rng(B),relation_dom(A)) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f36,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f42,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f45,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f46,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
( ! [A,B] :
( ( ~ in(sK0_skl(B,A),B)
& in(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f47]) ).
fof(f50,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f51,plain,
! [X0,X1] :
( ~ in(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f52,plain,
! [A] :
( ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f53,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| in(C,B) )
& ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| in(C,B) )
& ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ! [C] :
( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f55,plain,
! [A] :
( ( ! [B] :
( ( ( ( sK2_skl(B,A) = apply(A,sK3_skl(B,A))
& in(sK3_skl(B,A),relation_dom(A)) )
| in(sK2_skl(B,A),B) )
& ( ! [D] :
( sK2_skl(B,A) != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(sK2_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ! [C] :
( ( C = apply(A,sK1_skl(C,B,A))
& in(sK1_skl(C,B,A),relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(D,sK1_skl(C,B,A)),skolemize(C,sK2_skl(B,A)),skolemize(D,sK3_skl(B,A))],[f54]) ).
fof(f56,plain,
! [X0,X1,X2] :
( in(sK1_skl(X2,X1,X0),relation_dom(X0))
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [X0,X1,X2] :
( X2 = apply(X0,sK1_skl(X2,X1,X0))
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f83,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f84,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f86,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f87,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f92,plain,
( function(sK5_skl)
& relation(sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(A,sK5_skl)],[f19]) ).
fof(f93,plain,
relation(sK5_skl),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f95,plain,
( relation(sK6_skl)
& empty(sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(A,sK6_skl)],[f20]) ).
fof(f96,plain,
empty(sK6_skl),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f97,plain,
relation(sK6_skl),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f104,plain,
( relation(sK9_skl)
& ~ empty(sK9_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(A,sK9_skl)],[f23]) ).
fof(f106,plain,
relation(sK9_skl),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f107,plain,
! [A] :
( empty(sK10_skl(A))
& element(sK10_skl(A),powerset(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(B,sK10_skl(A))],[f24]) ).
fof(f108,plain,
! [X0] : element(sK10_skl(X0),powerset(X0)),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f109,plain,
! [X0] : empty(sK10_skl(X0)),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f119,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)],[f29]) ).
fof(f120,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)],[f119]) ).
fof(f121,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)],[f120]) ).
fof(f123,plain,
! [X0,X1,X2] :
( in(apply(X1,X2),relation_dom(X0))
| ~ in(X2,relation_dom(relation_composition(X1,X0)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f125,plain,
? [A] :
( ? [B] :
( ~ subset(relation_rng(B),relation_dom(A))
& relation_dom(relation_composition(B,A)) = relation_dom(B)
& function(B)
& relation(B) )
& function(A)
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f126,plain,
( ~ subset(relation_rng(sK14_skl),relation_dom(sK13_skl))
& relation_dom(relation_composition(sK14_skl,sK13_skl)) = relation_dom(sK14_skl)
& function(sK14_skl)
& relation(sK14_skl)
& function(sK13_skl)
& relation(sK13_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(A,sK13_skl),skolemize(B,sK14_skl)],[f125]) ).
fof(f127,plain,
relation(sK13_skl),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f128,plain,
function(sK13_skl),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f129,plain,
relation(sK14_skl),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f130,plain,
function(sK14_skl),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f131,plain,
relation_dom(relation_composition(sK14_skl,sK13_skl)) = relation_dom(sK14_skl),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f132,plain,
~ subset(relation_rng(sK14_skl),relation_dom(sK13_skl)),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f145,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f146,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f147,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f148,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f147]) ).
fof(f149,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f153,plain,
! [X0,X1] :
( in(sK1_skl(X1,relation_rng(X0),X0),relation_dom(X0))
| ~ in(X1,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f56]) ).
fof(f154,plain,
! [X0,X1] :
( X1 = apply(X0,sK1_skl(X1,relation_rng(X0),X0))
| ~ in(X1,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f57]) ).
fof(f176,definition,
( sQ4_spl
<=> relation(sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( sQ4_spl
| ~ relation(sK14_skl) ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f180,plain,
~ in(sK0_skl(relation_dom(sK13_skl),relation_rng(sK14_skl)),relation_dom(sK13_skl)),
inference(resolution,[status(thm)],[f132,f51]) ).
fof(f181,plain,
in(sK0_skl(relation_dom(sK13_skl),relation_rng(sK14_skl)),relation_rng(sK14_skl)),
inference(resolution,[status(thm)],[f132,f50]) ).
fof(f205,definition,
( sQ9_spl
<=> function(sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( sQ9_spl
| ~ function(sK14_skl) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,definition,
( sQ10_spl
<=> relation(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f210,plain,
( sQ10_spl
| ~ relation(sK13_skl) ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,definition,
( sQ11_spl
<=> function(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( sQ11_spl
| ~ function(sK13_skl) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f215,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f178,f129]) ).
fof(f216,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f215]) ).
fof(f217,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f213,f128]) ).
fof(f218,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f217]) ).
fof(f219,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f210,f127]) ).
fof(f220,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f219]) ).
fof(f221,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f207,f130]) ).
fof(f222,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f221]) ).
fof(f229,definition,
( sQ13_spl
<=> relation(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f231,plain,
( sQ13_spl
| ~ relation(sK9_skl) ),
inference(component_clause,[status(thm)],[f229]) ).
fof(f244,plain,
( sK0_skl(relation_dom(sK13_skl),relation_rng(sK14_skl)) = apply(sK14_skl,sK1_skl(sK0_skl(relation_dom(sK13_skl),relation_rng(sK14_skl)),relation_rng(sK14_skl),sK14_skl))
| ~ function(sK14_skl)
| ~ relation(sK14_skl) ),
inference(resolution,[status(thm)],[f181,f154]) ).
fof(f245,plain,
( in(sK1_skl(sK0_skl(relation_dom(sK13_skl),relation_rng(sK14_skl)),relation_rng(sK14_skl),sK14_skl),relation_dom(sK14_skl))
| ~ function(sK14_skl)
| ~ relation(sK14_skl) ),
inference(resolution,[status(thm)],[f181,f153]) ).
fof(f247,definition,
( sQ16_spl
<=> sK0_skl(relation_dom(sK13_skl),relation_rng(sK14_skl)) = apply(sK14_skl,sK1_skl(sK0_skl(relation_dom(sK13_skl),relation_rng(sK14_skl)),relation_rng(sK14_skl),sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f248,plain,
( ~ sQ16_spl
| sK0_skl(relation_dom(sK13_skl),relation_rng(sK14_skl)) = apply(sK14_skl,sK1_skl(sK0_skl(relation_dom(sK13_skl),relation_rng(sK14_skl)),relation_rng(sK14_skl),sK14_skl)) ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,plain,
( sQ16_spl
| ~ sQ9_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f244,f176,f205,f247]) ).
fof(f251,definition,
( sQ17_spl
<=> in(sK1_skl(sK0_skl(relation_dom(sK13_skl),relation_rng(sK14_skl)),relation_rng(sK14_skl),sK14_skl),relation_dom(sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f252,plain,
( ~ sQ17_spl
| in(sK1_skl(sK0_skl(relation_dom(sK13_skl),relation_rng(sK14_skl)),relation_rng(sK14_skl),sK14_skl),relation_dom(sK14_skl)) ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f254,plain,
( sQ17_spl
| ~ sQ9_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f245,f176,f205,f251]) ).
fof(f258,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f106,f231]) ).
fof(f259,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f258]) ).
fof(f297,plain,
! [X0] :
( in(apply(sK14_skl,X0),relation_dom(sK13_skl))
| ~ in(X0,relation_dom(sK14_skl))
| ~ function(sK14_skl)
| ~ relation(sK14_skl)
| ~ function(sK13_skl)
| ~ relation(sK13_skl) ),
inference(paramodulation,[status(thm)],[f131,f123]) ).
fof(f299,definition,
! [X0] :
( sQ22_spl
<=> ( in(apply(sK14_skl,X0),relation_dom(sK13_skl))
| ~ in(X0,relation_dom(sK14_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f300,plain,
! [X0] :
( ~ sQ22_spl
| in(apply(sK14_skl,X0),relation_dom(sK13_skl))
| ~ in(X0,relation_dom(sK14_skl)) ),
inference(component_clause,[status(thm)],[f299]) ).
fof(f302,plain,
( sQ22_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f297,f208,f211,f176,f205,f299]) ).
fof(f338,plain,
! [X0] : sK10_skl(X0) = empty_set,
inference(resolution,[status(thm)],[f146,f109]) ).
fof(f340,plain,
sK6_skl = empty_set,
inference(resolution,[status(thm)],[f146,f96]) ).
fof(f341,plain,
! [X0] :
( ~ empty(X0)
| relation_rng(X0) = empty_set ),
inference(resolution,[status(thm)],[f146,f87]) ).
fof(f387,plain,
~ empty(relation_rng(sK14_skl)),
inference(resolution,[status(thm)],[f149,f181]) ).
fof(f398,plain,
~ empty(sK14_skl),
inference(resolution,[status(thm)],[f387,f87]) ).
fof(f438,plain,
! [X0] : element(sK6_skl,powerset(X0)),
inference(backward_demodulation,[status(thm)],[f440,f108]) ).
fof(f440,plain,
! [X0] : sK10_skl(X0) = sK6_skl,
inference(forward_demodulation,[status(thm)],[f340,f338]) ).
fof(f462,definition,
( sQ36_spl
<=> relation(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( sQ36_spl
| ~ relation(sK5_skl) ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f478,plain,
( sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f464,f93]) ).
fof(f479,plain,
sQ36_spl,
inference(contradiction_clause,[status(thm)],[f478]) ).
fof(f545,plain,
! [X0] :
( ~ empty(X0)
| relation_rng(X0) = sK6_skl ),
inference(forward_demodulation,[status(thm)],[f340,f341]) ).
fof(f546,plain,
relation_rng(sK6_skl) = sK6_skl,
inference(resolution,[status(thm)],[f545,f96]) ).
fof(f567,definition,
( sQ49_spl
<=> relation(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f569,plain,
( sQ49_spl
| ~ relation(sK6_skl) ),
inference(component_clause,[status(thm)],[f567]) ).
fof(f570,definition,
( sQ50_spl
<=> relation(relation_rng(sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f572,plain,
( sQ50_spl
| ~ relation(relation_rng(sK6_skl)) ),
inference(component_clause,[status(thm)],[f570]) ).
fof(f573,definition,
( sQ51_spl
<=> empty(relation_dom(sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f575,plain,
( sQ51_spl
| ~ empty(relation_dom(sK6_skl)) ),
inference(component_clause,[status(thm)],[f573]) ).
fof(f577,definition,
( sQ52_spl
<=> function(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f579,plain,
( sQ52_spl
| ~ function(sK6_skl) ),
inference(component_clause,[status(thm)],[f577]) ).
fof(f598,plain,
( sQ50_spl
| ~ relation(sK6_skl) ),
inference(forward_demodulation,[status(thm)],[f546,f572]) ).
fof(f599,plain,
( sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f598,f97]) ).
fof(f600,plain,
sQ50_spl,
inference(contradiction_clause,[status(thm)],[f599]) ).
fof(f602,plain,
( sQ52_spl
| ~ empty(sK6_skl) ),
inference(resolution,[status(thm)],[f579,f42]) ).
fof(f603,plain,
( sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f602,f96]) ).
fof(f604,plain,
sQ52_spl,
inference(contradiction_clause,[status(thm)],[f603]) ).
fof(f605,plain,
( sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f569,f97]) ).
fof(f606,plain,
sQ49_spl,
inference(contradiction_clause,[status(thm)],[f605]) ).
fof(f670,plain,
( sQ51_spl
| ~ empty(sK6_skl) ),
inference(resolution,[status(thm)],[f575,f84]) ).
fof(f672,plain,
( sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f670,f96]) ).
fof(f673,plain,
sQ51_spl,
inference(contradiction_clause,[status(thm)],[f672]) ).
fof(f825,definition,
( sQ73_spl
<=> sK14_skl = sK6_skl ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f826,plain,
( ~ sQ73_spl
| sK14_skl = sK6_skl ),
inference(component_clause,[status(thm)],[f825]) ).
fof(f849,plain,
( ~ sQ73_spl
| empty(sK14_skl) ),
inference(backward_demodulation,[status(thm)],[f826,f96]) ).
fof(f852,plain,
( ~ sQ73_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f849,f398]) ).
fof(f853,plain,
~ sQ73_spl,
inference(contradiction_clause,[status(thm)],[f852]) ).
fof(f1036,definition,
! [X0] :
( sQ81_spl
<=> ( ~ empty(X0)
| ~ element(sK6_skl,powerset(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1037,plain,
! [X0] :
( ~ sQ81_spl
| ~ empty(X0)
| ~ element(sK6_skl,powerset(X0)) ),
inference(component_clause,[status(thm)],[f1036]) ).
fof(f1046,plain,
! [X0] :
( ~ sQ81_spl
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1037,f438]) ).
fof(f1052,plain,
( ~ sQ81_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f96,f1046]) ).
fof(f1053,plain,
~ sQ81_spl,
inference(contradiction_clause,[status(thm)],[f1052]) ).
fof(f1251,plain,
( ~ sQ22_spl
| ~ sQ17_spl
| in(apply(sK14_skl,sK1_skl(sK0_skl(relation_dom(sK13_skl),relation_rng(sK14_skl)),relation_rng(sK14_skl),sK14_skl)),relation_dom(sK13_skl)) ),
inference(resolution,[status(thm)],[f252,f300]) ).
fof(f1259,plain,
( ~ sQ22_spl
| ~ sQ17_spl
| ~ sQ16_spl
| in(sK0_skl(relation_dom(sK13_skl),relation_rng(sK14_skl)),relation_dom(sK13_skl)) ),
inference(forward_demodulation,[status(thm)],[f248,f1251]) ).
fof(f1260,plain,
( ~ sQ22_spl
| ~ sQ17_spl
| ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1259,f180]) ).
fof(f1261,plain,
( ~ sQ22_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f1260]) ).
fof(f1262,plain,
$false,
inference(sat_refutation,[status(thm)],[f216,f218,f220,f222,f250,f254,f259,f302,f479,f600,f604,f606,f673,f853,f1053,f1261]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU003+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:46:12 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.41 % Drodi V4.1.1
% 0.15/0.54 % Refutation found
% 0.15/0.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.56 % Elapsed time: 0.166863 seconds
% 0.15/0.56 % CPU time: 0.951323 seconds
% 0.15/0.56 % Total memory used: 119.736 MB
% 0.15/0.56 % Net memory used: 117.369 MB
%------------------------------------------------------------------------------