%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU212+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 : n004.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 02:19:41 PM UTC 2026
% Result : Theorem 0.18s 0.49s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 5 unt; 5 def)
% Number of atoms : 210 ( 44 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 255 ( 94 ~; 102 |; 37 &)
% ( 15 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 82 ( 65 !; 17 ?)
% 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(f6,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( B = apply(C,A)
& in(A,relation_dom(C)) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f44,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(f45,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)],[f44]) ).
fof(f46,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)],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( in(ordered_pair(X1,X2),X0)
| X2 != apply(X0,X1)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| X2 = apply(X0,X1)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f51,plain,
! [A] :
( ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f52,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B = relation_dom(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B = relation_dom(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ! [C] :
( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f52]) ).
fof(f54,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK1_skl(B,A),sK2_skl(B,A)),A)
| in(sK1_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(sK1_skl(B,A),D),A)
| ~ in(sK1_skl(B,A),B) ) )
| B = relation_dom(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(C,sK0_skl(C,B,A)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(D,sK0_skl(C,B,A)),skolemize(C,sK1_skl(B,A)),skolemize(D,sK2_skl(B,A))],[f53]) ).
fof(f56,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f104,plain,
? [A,B,C] :
( ( in(ordered_pair(A,B),C)
<~> ( B = apply(C,A)
& in(A,relation_dom(C)) ) )
& function(C)
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f105,plain,
? [A,B,C] :
( ( B != apply(C,A)
| ~ in(A,relation_dom(C))
| ~ in(ordered_pair(A,B),C) )
& ( ( B = apply(C,A)
& in(A,relation_dom(C)) )
| in(ordered_pair(A,B),C) )
& function(C)
& relation(C) ),
inference(NNF_transformation,[status(thm)],[f104]) ).
fof(f106,plain,
? [C] :
( ? [A,B] :
( ( B != apply(C,A)
| ~ in(A,relation_dom(C))
| ~ in(ordered_pair(A,B),C) )
& ( ( B = apply(C,A)
& in(A,relation_dom(C)) )
| in(ordered_pair(A,B),C) ) )
& function(C)
& relation(C) ),
inference(miniscoping,[status(thm)],[f105]) ).
fof(f107,plain,
( ( sK12_skl != apply(sK10_skl,sK11_skl)
| ~ in(sK11_skl,relation_dom(sK10_skl))
| ~ in(ordered_pair(sK11_skl,sK12_skl),sK10_skl) )
& ( ( sK12_skl = apply(sK10_skl,sK11_skl)
& in(sK11_skl,relation_dom(sK10_skl)) )
| in(ordered_pair(sK11_skl,sK12_skl),sK10_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)],[f106]) ).
fof(f108,plain,
relation(sK10_skl),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f109,plain,
function(sK10_skl),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f110,plain,
( in(sK11_skl,relation_dom(sK10_skl))
| in(ordered_pair(sK11_skl,sK12_skl),sK10_skl) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f111,plain,
( sK12_skl = apply(sK10_skl,sK11_skl)
| in(ordered_pair(sK11_skl,sK12_skl),sK10_skl) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f112,plain,
( sK12_skl != apply(sK10_skl,sK11_skl)
| ~ in(sK11_skl,relation_dom(sK10_skl))
| ~ in(ordered_pair(sK11_skl,sK12_skl),sK10_skl) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f113,definition,
( sQ0_spl
<=> in(ordered_pair(sK11_skl,sK12_skl),sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ0_spl
| in(ordered_pair(sK11_skl,sK12_skl),sK10_skl) ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,definition,
( sQ1_spl
<=> in(sK11_skl,relation_dom(sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f110,f113,f116]) ).
fof(f120,definition,
( sQ2_spl
<=> sK12_skl = apply(sK10_skl,sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f121,plain,
( ~ sQ2_spl
| sK12_skl = apply(sK10_skl,sK11_skl) ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f123,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f111,f113,f120]) ).
fof(f124,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f112,f113,f116,f120]) ).
fof(f125,plain,
! [X0,X1] :
( in(ordered_pair(X1,apply(X0,X1)),X0)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f47]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f56]) ).
fof(f134,plain,
( ~ sQ0_spl
| in(sK11_skl,relation_dom(sK10_skl))
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f129,f114]) ).
fof(f135,definition,
( sQ3_spl
<=> relation(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( sQ3_spl
| ~ relation(sK10_skl) ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f134,f135,f116,f113]) ).
fof(f142,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| X1 = apply(X0,X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f48,f129]) ).
fof(f155,plain,
( ~ sQ2_spl
| in(ordered_pair(sK11_skl,sK12_skl),sK10_skl)
| ~ in(sK11_skl,relation_dom(sK10_skl))
| ~ function(sK10_skl)
| ~ relation(sK10_skl) ),
inference(paramodulation,[status(thm)],[f121,f125]) ).
fof(f156,definition,
( sQ4_spl
<=> function(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( sQ4_spl
| ~ function(sK10_skl) ),
inference(component_clause,[status(thm)],[f156]) ).
fof(f163,plain,
( ~ sQ2_spl
| sQ0_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f155,f135,f156,f116,f113,f120]) ).
fof(f164,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f137,f108]) ).
fof(f165,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f164]) ).
fof(f167,plain,
( ~ sQ0_spl
| sK12_skl = apply(sK10_skl,sK11_skl)
| ~ function(sK10_skl)
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f114,f142]) ).
fof(f170,plain,
( ~ sQ0_spl
| sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f167,f135,f156,f120,f113]) ).
fof(f172,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f158,f109]) ).
fof(f173,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f172]) ).
fof(f174,plain,
$false,
inference(sat_refutation,[status(thm)],[f119,f123,f124,f138,f163,f165,f170,f173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU212+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n004.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 05:58:20 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.46 % Drodi V4.1.1
% 0.18/0.49 % Refutation found
% 0.18/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.54 % Elapsed time: 0.082219 seconds
% 0.26/0.54 % CPU time: 0.224313 seconds
% 0.26/0.54 % Total memory used: 102.699 MB
% 0.26/0.54 % Net memory used: 102.642 MB
%------------------------------------------------------------------------------