%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU193+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 : 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 02:19:36 PM UTC 2026
% Result : Theorem 6.58s 1.48s
% Output : CNFRefutation 6.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 7 unt; 4 def)
% Number of atoms : 175 ( 9 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 212 ( 84 ~; 86 |; 24 &)
% ( 10 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 93 ( 83 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( relation(C)
=> ( C = relation_dom_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),A)
& in(D,B) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
=> in(ordered_pair(C,D),B) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f175,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_dom_restriction(B,A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f176,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_dom_restriction(B,A),B) ),
inference(negated_conjecture,[status(cth)],[f175]) ).
fof(f208,plain,
! [A] :
( ! [B,C] :
( ( C = relation_dom_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),A)
& in(D,B) ) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f209,plain,
! [A] :
( ! [B,C] :
( ( ( ? [D,E] :
( ( ( in(ordered_pair(D,E),A)
& in(D,B) )
| in(ordered_pair(D,E),C) )
& ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_dom_restriction(A,B) )
& ( ! [D,E] :
( ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| in(ordered_pair(D,E),C) )
& ( ( in(ordered_pair(D,E),A)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_dom_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f208]) ).
fof(f210,plain,
! [A] :
( ! [C] :
( ( ! [B] :
( ? [D,E] :
( ( ( in(ordered_pair(D,E),A)
& in(D,B) )
| in(ordered_pair(D,E),C) )
& ( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| ~ in(ordered_pair(D,E),C) ) )
| C = relation_dom_restriction(A,B) )
& ! [B] :
( ( ! [D,E] :
( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(D,E),A)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_dom_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f209]) ).
fof(f211,plain,
! [A] :
( ! [C] :
( ( ! [B] :
( ( ( ( in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),A)
& in(sK2_skl(B,C,A),B) )
| in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),C) )
& ( ~ in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),A)
| ~ in(sK2_skl(B,C,A),B)
| ~ in(ordered_pair(sK2_skl(B,C,A),sK3_skl(B,C,A)),C) ) )
| C = relation_dom_restriction(A,B) )
& ! [B] :
( ( ! [D,E] :
( ~ in(ordered_pair(D,E),A)
| ~ in(D,B)
| in(ordered_pair(D,E),C) )
& ! [D,E] :
( ( in(ordered_pair(D,E),A)
& in(D,B) )
| ~ in(ordered_pair(D,E),C) ) )
| C != relation_dom_restriction(A,B) ) )
| ~ relation(C) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(D,sK2_skl(B,C,A)),skolemize(E,sK3_skl(B,C,A))],[f210]) ).
fof(f213,plain,
! [X0,X1,X2,X3,X4] :
( in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X3,X4),X1)
| X1 != relation_dom_restriction(X0,X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f290,plain,
! [A] :
( ! [B] :
( ( subset(A,B)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f291,plain,
! [A] :
( ! [B] :
( ( ( ? [C,D] :
( ~ in(ordered_pair(C,D),B)
& in(ordered_pair(C,D),A) )
| subset(A,B) )
& ( ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) )
| ~ subset(A,B) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f290]) ).
fof(f292,plain,
! [A] :
( ! [B] :
( ( ( ( ~ in(ordered_pair(sK20_skl(B,A),sK21_skl(B,A)),B)
& in(ordered_pair(sK20_skl(B,A),sK21_skl(B,A)),A) )
| subset(A,B) )
& ( ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) )
| ~ subset(A,B) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl]),skolemize(C,sK20_skl(B,A)),skolemize(D,sK21_skl(B,A))],[f291]) ).
fof(f294,plain,
! [X0,X1] :
( in(ordered_pair(sK20_skl(X1,X0),sK21_skl(X1,X0)),X0)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f292]) ).
fof(f295,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK20_skl(X1,X0),sK21_skl(X1,X0)),X1)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f292]) ).
fof(f401,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f402,plain,
! [A] :
( ! [B] : relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f401]) ).
fof(f403,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f402]) ).
fof(f708,plain,
? [A,B] :
( ~ subset(relation_dom_restriction(B,A),B)
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f176]) ).
fof(f709,plain,
? [B] :
( ? [A] : ~ subset(relation_dom_restriction(B,A),B)
& relation(B) ),
inference(miniscoping,[status(thm)],[f708]) ).
fof(f710,plain,
( ~ subset(relation_dom_restriction(sK55_skl,sK56_skl),sK55_skl)
& relation(sK55_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl,sK56_skl]),skolemize(B,sK55_skl),skolemize(A,sK56_skl)],[f709]) ).
fof(f711,plain,
relation(sK55_skl),
inference(cnf_transformation,[status(thm)],[f710]) ).
fof(f712,plain,
~ subset(relation_dom_restriction(sK55_skl,sK56_skl),sK55_skl),
inference(cnf_transformation,[status(thm)],[f710]) ).
fof(f747,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X2,X3),relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f213]) ).
fof(f795,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X1,X2),relation_dom_restriction(X0,X3))
| ~ relation(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f747,f403]) ).
fof(f797,plain,
! [X0] : relation(relation_dom_restriction(sK55_skl,X0)),
inference(resolution,[status(thm)],[f403,f711]) ).
fof(f1656,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK20_skl(X2,relation_dom_restriction(X0,X1)),sK21_skl(X2,relation_dom_restriction(X0,X1))),X0)
| ~ relation(X0)
| subset(relation_dom_restriction(X0,X1),X2)
| ~ relation(X2)
| ~ relation(relation_dom_restriction(X0,X1)) ),
inference(resolution,[status(thm)],[f294,f795]) ).
fof(f1669,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK20_skl(X0,relation_dom_restriction(X1,X2)),sK21_skl(X0,relation_dom_restriction(X1,X2))),X1)
| ~ relation(X1)
| subset(relation_dom_restriction(X1,X2),X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1656,f403]) ).
fof(f3723,plain,
( in(ordered_pair(sK20_skl(sK55_skl,relation_dom_restriction(sK55_skl,sK56_skl)),sK21_skl(sK55_skl,relation_dom_restriction(sK55_skl,sK56_skl))),sK55_skl)
| ~ relation(sK55_skl)
| ~ relation(sK55_skl) ),
inference(resolution,[status(thm)],[f1669,f712]) ).
fof(f3742,definition,
( sQ108_spl
<=> relation(sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f3744,plain,
( sQ108_spl
| ~ relation(sK55_skl) ),
inference(component_clause,[status(thm)],[f3742]) ).
fof(f3745,definition,
( sQ109_spl
<=> in(ordered_pair(sK20_skl(sK55_skl,relation_dom_restriction(sK55_skl,sK56_skl)),sK21_skl(sK55_skl,relation_dom_restriction(sK55_skl,sK56_skl))),sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f3746,plain,
( ~ sQ109_spl
| in(ordered_pair(sK20_skl(sK55_skl,relation_dom_restriction(sK55_skl,sK56_skl)),sK21_skl(sK55_skl,relation_dom_restriction(sK55_skl,sK56_skl))),sK55_skl) ),
inference(component_clause,[status(thm)],[f3745]) ).
fof(f3748,plain,
( sQ109_spl
| ~ sQ108_spl ),
inference(split_clause,[status(thm)],[f3723,f3742,f3745]) ).
fof(f3758,plain,
( sQ108_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3744,f711]) ).
fof(f3759,plain,
sQ108_spl,
inference(contradiction_clause,[status(thm)],[f3758]) ).
fof(f3769,plain,
( ~ sQ109_spl
| subset(relation_dom_restriction(sK55_skl,sK56_skl),sK55_skl)
| ~ relation(sK55_skl)
| ~ relation(relation_dom_restriction(sK55_skl,sK56_skl)) ),
inference(resolution,[status(thm)],[f3746,f295]) ).
fof(f3776,definition,
( sQ112_spl
<=> relation(relation_dom_restriction(sK55_skl,sK56_skl)) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f3778,plain,
( sQ112_spl
| ~ relation(relation_dom_restriction(sK55_skl,sK56_skl)) ),
inference(component_clause,[status(thm)],[f3776]) ).
fof(f3779,definition,
( sQ113_spl
<=> subset(relation_dom_restriction(sK55_skl,sK56_skl),sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f3780,plain,
( ~ sQ113_spl
| subset(relation_dom_restriction(sK55_skl,sK56_skl),sK55_skl) ),
inference(component_clause,[status(thm)],[f3779]) ).
fof(f3782,plain,
( ~ sQ109_spl
| sQ113_spl
| ~ sQ108_spl
| ~ sQ112_spl ),
inference(split_clause,[status(thm)],[f3769,f3776,f3742,f3779,f3745]) ).
fof(f3799,plain,
( sQ112_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3778,f797]) ).
fof(f3800,plain,
sQ112_spl,
inference(contradiction_clause,[status(thm)],[f3799]) ).
fof(f3801,plain,
( ~ sQ113_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3780,f712]) ).
fof(f3802,plain,
~ sQ113_spl,
inference(contradiction_clause,[status(thm)],[f3801]) ).
fof(f3803,plain,
$false,
inference(sat_refutation,[status(thm)],[f3748,f3759,f3782,f3800,f3802]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU193+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.53 % Computer : n014.cluster.edu
% 0.11/0.53 % Model : x86_64 x86_64
% 0.11/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.53 % Memory : 8046.5625MB
% 0.11/0.53 % OS : Linux 6.8.0-71-generic
% 0.11/0.53 % CPULimit : 300
% 0.11/0.53 % WCLimit : 300
% 0.11/0.53 % DateTime : Mon Sep 21 05:56:38 UTC 2026
% 0.11/0.53 % CPUTime :
% 0.11/0.56 % Drodi V4.1.1
% 6.58/1.48 % Refutation found
% 6.58/1.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 6.58/1.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.58/1.49 % Elapsed time: 0.951988 seconds
% 6.58/1.49 % CPU time: 7.246007 seconds
% 6.58/1.49 % Total memory used: 185.757 MB
% 6.58/1.49 % Net memory used: 172.336 MB
%------------------------------------------------------------------------------