%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU177+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 02:19:33 PM UTC 2026
% Result : Theorem 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 4 unt; 3 def)
% Number of atoms : 142 ( 18 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 172 ( 64 ~; 65 |; 26 &)
% ( 11 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 92 ( 70 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,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(f21,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f94,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_rng(C))
& in(A,relation_dom(C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_rng(C))
& in(A,relation_dom(C)) ) ) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f237,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)],[f17]) ).
fof(f238,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)],[f237]) ).
fof(f239,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)],[f238]) ).
fof(f240,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK16_skl(B,A),sK17_skl(B,A)),A)
| in(sK16_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(sK16_skl(B,A),D),A)
| ~ in(sK16_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,sK15_skl(C,B,A)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl,sK17_skl]),skolemize(D,sK15_skl(C,B,A)),skolemize(C,sK16_skl(B,A)),skolemize(D,sK17_skl(B,A))],[f239]) ).
fof(f242,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)],[f240]) ).
fof(f264,plain,
! [A] :
( ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f265,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(D,C),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f264]) ).
fof(f266,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] : in(ordered_pair(D,C),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f265]) ).
fof(f267,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK24_skl(B,A),sK23_skl(B,A)),A)
| in(sK23_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(D,sK23_skl(B,A)),A)
| ~ in(sK23_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(sK22_skl(C,B,A),C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22_skl,sK23_skl,sK24_skl]),skolemize(D,sK22_skl(C,B,A)),skolemize(C,sK23_skl(B,A)),skolemize(D,sK24_skl(B,A))],[f266]) ).
fof(f269,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X3,X2),X0)
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f419,plain,
? [A,B,C] :
( ( ~ in(B,relation_rng(C))
| ~ in(A,relation_dom(C)) )
& in(ordered_pair(A,B),C)
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f95]) ).
fof(f420,plain,
? [C] :
( ? [A,B] :
( ( ~ in(B,relation_rng(C))
| ~ in(A,relation_dom(C)) )
& in(ordered_pair(A,B),C) )
& relation(C) ),
inference(miniscoping,[status(thm)],[f419]) ).
fof(f421,plain,
( ( ~ in(sK36_skl,relation_rng(sK34_skl))
| ~ in(sK35_skl,relation_dom(sK34_skl)) )
& in(ordered_pair(sK35_skl,sK36_skl),sK34_skl)
& relation(sK34_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34_skl,sK35_skl,sK36_skl]),skolemize(C,sK34_skl),skolemize(A,sK35_skl),skolemize(B,sK36_skl)],[f420]) ).
fof(f422,plain,
relation(sK34_skl),
inference(cnf_transformation,[status(thm)],[f421]) ).
fof(f423,plain,
in(ordered_pair(sK35_skl,sK36_skl),sK34_skl),
inference(cnf_transformation,[status(thm)],[f421]) ).
fof(f424,plain,
( ~ in(sK36_skl,relation_rng(sK34_skl))
| ~ in(sK35_skl,relation_dom(sK34_skl)) ),
inference(cnf_transformation,[status(thm)],[f421]) ).
fof(f561,definition,
( sQ0_spl
<=> in(sK35_skl,relation_dom(sK34_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f564,definition,
( sQ1_spl
<=> in(sK36_skl,relation_rng(sK34_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f567,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f424,f561,f564]) ).
fof(f592,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f242]) ).
fof(f600,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f269]) ).
fof(f612,plain,
( in(sK35_skl,relation_dom(sK34_skl))
| ~ relation(sK34_skl) ),
inference(resolution,[status(thm)],[f592,f423]) ).
fof(f613,definition,
( sQ2_spl
<=> relation(sK34_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f615,plain,
( sQ2_spl
| ~ relation(sK34_skl) ),
inference(component_clause,[status(thm)],[f613]) ).
fof(f616,plain,
( sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f612,f613,f561]) ).
fof(f617,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f615,f422]) ).
fof(f618,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f617]) ).
fof(f620,plain,
( in(sK36_skl,relation_rng(sK34_skl))
| ~ relation(sK34_skl) ),
inference(resolution,[status(thm)],[f600,f423]) ).
fof(f621,plain,
( sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f620,f613,f564]) ).
fof(f622,plain,
$false,
inference(sat_refutation,[status(thm)],[f567,f616,f618,f621]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU177+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n006.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 05:54:27 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.058852 seconds
% 0.13/0.42 % CPU time: 0.145409 seconds
% 0.13/0.42 % Total memory used: 80.029 MB
% 0.13/0.42 % Net memory used: 79.916 MB
%------------------------------------------------------------------------------