%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET991+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 02:11:06 PM UTC 2026
% Result : Theorem 0.15s 15.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 8 unt; 3 def)
% Number of atoms : 122 ( 24 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 142 ( 51 ~; 50 |; 29 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 47 ( 35 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f30,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( in(A,relation_dom(B))
=> in(apply(B,A),relation_rng(B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ( in(A,relation_dom(B))
=> in(apply(B,A),relation_rng(B)) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f32,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/sandbox/benchmark/theBenchmark.p') ).
fof(f105,plain,
? [A,B] :
( ~ in(apply(B,A),relation_rng(B))
& in(A,relation_dom(B))
& function(B)
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f106,plain,
? [B] :
( ? [A] :
( ~ in(apply(B,A),relation_rng(B))
& in(A,relation_dom(B)) )
& function(B)
& relation(B) ),
inference(miniscoping,[status(thm)],[f105]) ).
fof(f107,plain,
( ~ in(apply(sK9_skl,sK10_skl),relation_rng(sK9_skl))
& in(sK10_skl,relation_dom(sK9_skl))
& function(sK9_skl)
& relation(sK9_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl]),skolemize(B,sK9_skl),skolemize(A,sK10_skl)],[f106]) ).
fof(f108,plain,
relation(sK9_skl),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f109,plain,
function(sK9_skl),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f110,plain,
in(sK10_skl,relation_dom(sK9_skl)),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f111,plain,
~ in(apply(sK9_skl,sK10_skl),relation_rng(sK9_skl)),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f112,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)],[f32]) ).
fof(f113,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)],[f112]) ).
fof(f114,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)],[f113]) ).
fof(f115,plain,
! [A] :
( ( ! [B] :
( ( ( ( sK12_skl(B,A) = apply(A,sK13_skl(B,A))
& in(sK13_skl(B,A),relation_dom(A)) )
| in(sK12_skl(B,A),B) )
& ( ! [D] :
( sK12_skl(B,A) != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(sK12_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,sK11_skl(C,B,A))
& in(sK11_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,[sK11_skl,sK12_skl,sK13_skl]),skolemize(D,sK11_skl(C,B,A)),skolemize(C,sK12_skl(B,A)),skolemize(D,sK13_skl(B,A))],[f114]) ).
fof(f118,plain,
! [X0,X1,X2,X3] :
( X2 != apply(X0,X3)
| ~ in(X3,relation_dom(X0))
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f124,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(X0))
| in(apply(X0,X1),relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f118]) ).
fof(f137,plain,
( in(apply(sK9_skl,sK10_skl),relation_rng(sK9_skl))
| ~ function(sK9_skl)
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f124,f110]) ).
fof(f138,definition,
( sQ0_spl
<=> relation(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( sQ0_spl
| ~ relation(sK9_skl) ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f141,definition,
( sQ1_spl
<=> function(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f143,plain,
( sQ1_spl
| ~ function(sK9_skl) ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,definition,
( sQ2_spl
<=> in(apply(sK9_skl,sK10_skl),relation_rng(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f145,plain,
( ~ sQ2_spl
| in(apply(sK9_skl,sK10_skl),relation_rng(sK9_skl)) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f137,f138,f141,f144]) ).
fof(f148,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f145,f111]) ).
fof(f149,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f148]) ).
fof(f150,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f140,f108]) ).
fof(f151,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f150]) ).
fof(f152,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f143,f109]) ).
fof(f153,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f152]) ).
fof(f154,plain,
$false,
inference(sat_refutation,[status(thm)],[f147,f149,f151,f153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET991+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/15.39 % Computer : n002.cluster.edu
% 0.10/15.39 % Model : x86_64 x86_64
% 0.10/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.39 % Memory : 8046.5625MB
% 0.10/15.39 % OS : Linux 6.8.0-71-generic
% 0.10/15.39 % CPULimit : 300
% 0.10/15.39 % WCLimit : 300
% 0.10/15.39 % DateTime : Mon Sep 21 05:49:34 UTC 2026
% 0.10/15.39 % CPUTime :
% 0.15/15.40 % Drodi V4.1.1
% 0.15/15.42 % Refutation found
% 0.15/15.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/15.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/15.46 % Elapsed time: 0.053077 seconds
% 0.15/15.46 % CPU time: 0.150486 seconds
% 0.15/15.46 % Total memory used: 81.240 MB
% 0.15/15.46 % Net memory used: 81.134 MB
%------------------------------------------------------------------------------