%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU177+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 : n014.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 0.38s
% 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(f24,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(f25,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)],[f24]) ).
fof(f26,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(f27,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(f57,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)],[f25]) ).
fof(f58,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)],[f57]) ).
fof(f59,plain,
( ( ~ in(sK6_skl,relation_rng(sK4_skl))
| ~ in(sK5_skl,relation_dom(sK4_skl)) )
& in(ordered_pair(sK5_skl,sK6_skl),sK4_skl)
& relation(sK4_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl]),skolemize(C,sK4_skl),skolemize(A,sK5_skl),skolemize(B,sK6_skl)],[f58]) ).
fof(f60,plain,
relation(sK4_skl),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
in(ordered_pair(sK5_skl,sK6_skl),sK4_skl),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f62,plain,
( ~ in(sK6_skl,relation_rng(sK4_skl))
| ~ in(sK5_skl,relation_dom(sK4_skl)) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f63,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)],[f26]) ).
fof(f64,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)],[f63]) ).
fof(f65,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)],[f64]) ).
fof(f66,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK8_skl(B,A),sK9_skl(B,A)),A)
| in(sK8_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(sK8_skl(B,A),D),A)
| ~ in(sK8_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,sK7_skl(C,B,A)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl,sK9_skl]),skolemize(D,sK7_skl(C,B,A)),skolemize(C,sK8_skl(B,A)),skolemize(D,sK9_skl(B,A))],[f65]) ).
fof(f68,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)],[f66]) ).
fof(f71,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)],[f27]) ).
fof(f72,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)],[f71]) ).
fof(f73,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)],[f72]) ).
fof(f74,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK12_skl(B,A),sK11_skl(B,A)),A)
| in(sK11_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(D,sK11_skl(B,A)),A)
| ~ in(sK11_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(sK10_skl(C,B,A),C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl]),skolemize(D,sK10_skl(C,B,A)),skolemize(C,sK11_skl(B,A)),skolemize(D,sK12_skl(B,A))],[f73]) ).
fof(f76,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)],[f74]) ).
fof(f79,definition,
( sQ0_spl
<=> in(sK5_skl,relation_dom(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f82,definition,
( sQ1_spl
<=> in(sK6_skl,relation_rng(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f85,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f62,f79,f82]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f68]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X2,X1),X0)
| in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f76]) ).
fof(f91,plain,
( in(sK5_skl,relation_dom(sK4_skl))
| ~ relation(sK4_skl) ),
inference(resolution,[status(thm)],[f87,f61]) ).
fof(f92,definition,
( sQ2_spl
<=> relation(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( sQ2_spl
| ~ relation(sK4_skl) ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f95,plain,
( sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f91,f92,f79]) ).
fof(f96,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f94,f60]) ).
fof(f97,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f96]) ).
fof(f99,plain,
( in(sK6_skl,relation_rng(sK4_skl))
| ~ relation(sK4_skl) ),
inference(resolution,[status(thm)],[f89,f61]) ).
fof(f100,plain,
( sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f99,f92,f82]) ).
fof(f101,plain,
$false,
inference(sat_refutation,[status(thm)],[f85,f95,f97,f100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU177+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n014.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 05:54:34 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.062994 seconds
% 0.13/0.42 % CPU time: 0.154870 seconds
% 0.13/0.42 % Total memory used: 54.328 MB
% 0.13/0.42 % Net memory used: 54.153 MB
%------------------------------------------------------------------------------