%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU192+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 : n005.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 20.90s 8.18s
% Output : CNFRefutation 20.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 10
% Syntax : Number of formulae : 93 ( 12 unt; 0 def)
% Number of atoms : 414 ( 40 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 556 ( 235 ~; 228 |; 67 &)
% ( 15 <=>; 10 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-3 aty)
% Number of variables : 270 ( 245 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f17,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,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(f56,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,axiom,
! [A] : set_union2(A,empty_set) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f119,lemma,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
=> ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f173,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,relation_dom(C))
& in(A,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f174,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,relation_dom(C))
& in(A,B) ) ) ),
inference(negated_conjecture,[status(cth)],[f173]) ).
fof(f189,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f201,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f202,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(miniscoping,[status(thm)],[f201]) ).
fof(f203,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f206,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(f207,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)],[f206]) ).
fof(f208,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)],[f207]) ).
fof(f209,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))],[f208]) ).
fof(f210,plain,
! [X0,X1,X2,X3,X4] :
( in(X3,X2)
| ~ in(ordered_pair(X3,X4),X1)
| X1 != relation_dom_restriction(X0,X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f211,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)],[f209]) ).
fof(f212,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X2)
| in(ordered_pair(X3,X4),X1)
| X1 != relation_dom_restriction(X0,X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f270,plain,
! [A,B,C] :
( ( ? [D] :
( ( in(D,B)
| in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& ~ in(D,A) )
| ~ in(D,C) ) )
| C = set_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f17]) ).
fof(f271,plain,
( ! [A,B,C] :
( ? [D] :
( ( in(D,B)
| in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& ~ in(D,A) )
| ~ in(D,C) ) )
| C = set_union2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ! [D] :
( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(miniscoping,[status(thm)],[f270]) ).
fof(f272,plain,
( ! [A,B,C] :
( ( ( in(sK14_skl(C,B,A),B)
| in(sK14_skl(C,B,A),A)
| in(sK14_skl(C,B,A),C) )
& ( ( ~ in(sK14_skl(C,B,A),B)
& ~ in(sK14_skl(C,B,A),A) )
| ~ in(sK14_skl(C,B,A),C) ) )
| C = set_union2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ! [D] :
( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl]),skolemize(D,sK14_skl(C,B,A))],[f271]) ).
fof(f275,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f272]) ).
fof(f288,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f289,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f288]) ).
fof(f290,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f289]) ).
fof(f291,plain,
( ! [A,B] :
( ( ~ in(sK20_skl(B,A),B)
& in(sK20_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl]),skolemize(C,sK20_skl(B,A))],[f290]) ).
fof(f292,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f291]) ).
fof(f304,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)],[f21]) ).
fof(f305,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)],[f304]) ).
fof(f306,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)],[f305]) ).
fof(f307,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK23_skl(B,A),sK24_skl(B,A)),A)
| in(sK23_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(sK23_skl(B,A),D),A)
| ~ in(sK23_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,sK22_skl(C,B,A)),A)
| ~ in(C,B) ) )
| B != relation_dom(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))],[f306]) ).
fof(f308,plain,
! [X0,X1,X2] :
( in(ordered_pair(X2,sK22_skl(X2,X1,X0)),X0)
| ~ in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f307]) ).
fof(f309,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)],[f307]) ).
fof(f393,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f394,plain,
! [A] :
( ! [B] : relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f393]) ).
fof(f395,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f394]) ).
fof(f534,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f547,plain,
! [A] :
( ! [B] :
( ( subset(relation_rng(A),relation_rng(B))
& subset(relation_dom(A),relation_dom(B)) )
| ~ subset(A,B)
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f119]) ).
fof(f548,plain,
! [X0,X1] :
( subset(relation_dom(X0),relation_dom(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f547]) ).
fof(f694,plain,
? [A,B,C] :
( ( in(A,relation_dom(relation_dom_restriction(C,B)))
<~> ( in(A,relation_dom(C))
& in(A,B) ) )
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f174]) ).
fof(f695,plain,
? [A,B,C] :
( ( ~ in(A,relation_dom(C))
| ~ in(A,B)
| ~ in(A,relation_dom(relation_dom_restriction(C,B))) )
& ( ( in(A,relation_dom(C))
& in(A,B) )
| in(A,relation_dom(relation_dom_restriction(C,B))) )
& relation(C) ),
inference(NNF_transformation,[status(thm)],[f694]) ).
fof(f696,plain,
? [C] :
( ? [A,B] :
( ( ~ in(A,relation_dom(C))
| ~ in(A,B)
| ~ in(A,relation_dom(relation_dom_restriction(C,B))) )
& ( ( in(A,relation_dom(C))
& in(A,B) )
| in(A,relation_dom(relation_dom_restriction(C,B))) ) )
& relation(C) ),
inference(miniscoping,[status(thm)],[f695]) ).
fof(f697,plain,
( ( ~ in(sK54_skl,relation_dom(sK53_skl))
| ~ in(sK54_skl,sK55_skl)
| ~ in(sK54_skl,relation_dom(relation_dom_restriction(sK53_skl,sK55_skl))) )
& ( ( in(sK54_skl,relation_dom(sK53_skl))
& in(sK54_skl,sK55_skl) )
| in(sK54_skl,relation_dom(relation_dom_restriction(sK53_skl,sK55_skl))) )
& relation(sK53_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53_skl,sK54_skl,sK55_skl]),skolemize(C,sK53_skl),skolemize(A,sK54_skl),skolemize(B,sK55_skl)],[f696]) ).
fof(f698,plain,
relation(sK53_skl),
inference(cnf_transformation,[status(thm)],[f697]) ).
fof(f699,plain,
( in(sK54_skl,sK55_skl)
| in(sK54_skl,relation_dom(relation_dom_restriction(sK53_skl,sK55_skl))) ),
inference(cnf_transformation,[status(thm)],[f697]) ).
fof(f700,plain,
( in(sK54_skl,relation_dom(sK53_skl))
| in(sK54_skl,relation_dom(relation_dom_restriction(sK53_skl,sK55_skl))) ),
inference(cnf_transformation,[status(thm)],[f697]) ).
fof(f701,plain,
( ~ in(sK54_skl,relation_dom(sK53_skl))
| ~ in(sK54_skl,sK55_skl)
| ~ in(sK54_skl,relation_dom(relation_dom_restriction(sK53_skl,sK55_skl))) ),
inference(cnf_transformation,[status(thm)],[f697]) ).
fof(f733,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f203]) ).
fof(f735,plain,
! [X0,X1,X2,X3] :
( in(X2,X1)
| ~ in(ordered_pair(X2,X3),relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f210]) ).
fof(f736,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)],[f211]) ).
fof(f737,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1)
| in(ordered_pair(X2,X3),relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f212]) ).
fof(f753,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f275]) ).
fof(f759,plain,
! [X0,X1] :
( in(ordered_pair(X1,sK22_skl(X1,relation_dom(X0),X0)),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f308]) ).
fof(f760,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f309]) ).
fof(f788,plain,
! [X0,X1,X2,X3] :
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),relation_dom_restriction(X0,X3))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f735,f395]) ).
fof(f789,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X1,X2),relation_dom_restriction(X0,X3))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f736,f395]) ).
fof(f798,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X1,X2),X0)
| ~ in(X1,X3)
| in(ordered_pair(X1,X2),relation_dom_restriction(X0,X3))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f737,f395]) ).
fof(f806,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1)
| ~ relation(X0)
| in(X2,relation_dom(relation_dom_restriction(X0,X1)))
| ~ relation(relation_dom_restriction(X0,X1)) ),
inference(resolution,[status(thm)],[f760,f798]) ).
fof(f807,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X0,X3),X1)
| ~ in(X0,X2)
| ~ relation(X1)
| in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f806,f395]) ).
fof(f814,plain,
! [X0] :
( ~ in(sK54_skl,relation_dom(sK53_skl))
| ~ in(sK54_skl,sK55_skl)
| ~ in(ordered_pair(sK54_skl,X0),sK53_skl)
| ~ in(sK54_skl,sK55_skl)
| ~ relation(sK53_skl) ),
inference(resolution,[status(thm)],[f807,f701]) ).
fof(f816,plain,
! [X0] :
( ~ in(sK54_skl,relation_dom(sK53_skl))
| ~ in(ordered_pair(sK54_skl,X0),sK53_skl)
| ~ in(sK54_skl,sK55_skl)
| ~ relation(sK53_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f814]) ).
fof(f817,plain,
! [X0] :
( ~ in(sK54_skl,relation_dom(sK53_skl))
| ~ in(ordered_pair(sK54_skl,X0),sK53_skl)
| ~ in(sK54_skl,sK55_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f816,f698]) ).
fof(f1000,plain,
! [X0] : set_union2(empty_set,X0) = X0,
inference(paramodulation,[status(thm)],[f189,f534]) ).
fof(f2516,plain,
! [X0,X1,X2,X3] :
( in(X0,relation_dom(set_union2(X3,X2)))
| ~ relation(set_union2(X3,X2))
| ~ in(ordered_pair(X0,X1),X2) ),
inference(resolution,[status(thm)],[f753,f760]) ).
fof(f3112,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ relation(X2)
| ~ relation(X1)
| in(X0,relation_dom(X2))
| ~ in(X0,relation_dom(X1)) ),
inference(resolution,[status(thm)],[f292,f548]) ).
fof(f3920,plain,
( ~ in(sK54_skl,relation_dom(sK53_skl))
| ~ in(sK54_skl,sK55_skl)
| ~ in(sK54_skl,relation_dom(sK53_skl))
| ~ relation(sK53_skl) ),
inference(resolution,[status(thm)],[f759,f817]) ).
fof(f3922,plain,
! [X0,X1,X2] :
( in(ordered_pair(X2,sK22_skl(X2,relation_dom(relation_dom_restriction(X0,X1)),relation_dom_restriction(X0,X1))),X0)
| ~ relation(X0)
| ~ in(X2,relation_dom(relation_dom_restriction(X0,X1)))
| ~ relation(relation_dom_restriction(X0,X1)) ),
inference(resolution,[status(thm)],[f759,f789]) ).
fof(f3923,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ relation(X0)
| ~ in(X2,relation_dom(relation_dom_restriction(X0,X1)))
| ~ relation(relation_dom_restriction(X0,X1)) ),
inference(resolution,[status(thm)],[f759,f788]) ).
fof(f3948,plain,
( ~ in(sK54_skl,sK55_skl)
| ~ in(sK54_skl,relation_dom(sK53_skl))
| ~ relation(sK53_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f3920]) ).
fof(f3949,plain,
( ~ in(sK54_skl,sK55_skl)
| ~ in(sK54_skl,relation_dom(sK53_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f3948,f698]) ).
fof(f3953,plain,
! [X0,X1,X2] :
( in(ordered_pair(X0,sK22_skl(X0,relation_dom(relation_dom_restriction(X1,X2)),relation_dom_restriction(X1,X2))),X1)
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f3922,f395]) ).
fof(f3954,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f3923,f395]) ).
fof(f3980,plain,
! [X0] :
( ~ subset(X0,sK53_skl)
| ~ relation(sK53_skl)
| ~ relation(X0)
| ~ in(sK54_skl,relation_dom(X0))
| ~ in(sK54_skl,sK55_skl) ),
inference(resolution,[status(thm)],[f3949,f3112]) ).
fof(f3981,plain,
! [X0] :
( ~ subset(X0,sK53_skl)
| ~ relation(X0)
| ~ in(sK54_skl,relation_dom(X0))
| ~ in(sK54_skl,sK55_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f3980,f698]) ).
fof(f4381,plain,
( in(sK54_skl,sK55_skl)
| in(sK54_skl,sK55_skl)
| ~ relation(sK53_skl) ),
inference(resolution,[status(thm)],[f3954,f699]) ).
fof(f4389,plain,
( in(sK54_skl,sK55_skl)
| ~ relation(sK53_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f4381]) ).
fof(f4390,plain,
in(sK54_skl,sK55_skl),
inference(forward_subsumption_resolution,[status(thm)],[f4389,f698]) ).
fof(f4395,plain,
! [X0] :
( ~ subset(X0,sK53_skl)
| ~ relation(X0)
| ~ in(sK54_skl,relation_dom(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f3981,f4390]) ).
fof(f4396,plain,
~ in(sK54_skl,relation_dom(sK53_skl)),
inference(backward_subsumption_resolution,[status(thm)],[f3949,f4390]) ).
fof(f4558,plain,
in(sK54_skl,relation_dom(relation_dom_restriction(sK53_skl,sK55_skl))),
inference(backward_subsumption_resolution,[status(thm)],[f700,f4396]) ).
fof(f5064,plain,
! [X0,X1,X2] :
( ~ relation(set_union2(X0,X1))
| ~ in(ordered_pair(sK54_skl,X2),X1)
| ~ subset(set_union2(X0,X1),sK53_skl)
| ~ relation(set_union2(X0,X1)) ),
inference(resolution,[status(thm)],[f4395,f2516]) ).
fof(f5078,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK54_skl,X2),X1)
| ~ subset(set_union2(X0,X1),sK53_skl)
| ~ relation(set_union2(X0,X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f5064]) ).
fof(f5562,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK54_skl,X1),X0)
| ~ subset(X0,sK53_skl)
| ~ relation(set_union2(empty_set,X0)) ),
inference(paramodulation,[status(thm)],[f1000,f5078]) ).
fof(f5567,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK54_skl,X1),X0)
| ~ subset(X0,sK53_skl)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f1000,f5562]) ).
fof(f5835,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(sK54_skl,relation_dom(relation_dom_restriction(X0,X1)))
| ~ subset(X0,sK53_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f5567,f3953]) ).
fof(f5868,plain,
! [X0,X1] :
( ~ in(sK54_skl,relation_dom(relation_dom_restriction(X0,X1)))
| ~ subset(X0,sK53_skl)
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f5835]) ).
fof(f5871,plain,
( ~ subset(sK53_skl,sK53_skl)
| ~ relation(sK53_skl) ),
inference(resolution,[status(thm)],[f5868,f4558]) ).
fof(f5875,plain,
~ subset(sK53_skl,sK53_skl),
inference(forward_subsumption_resolution,[status(thm)],[f5871,f698]) ).
fof(f5879,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5875,f733]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU192+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.43 % Computer : n005.cluster.edu
% 0.15/5.43 % Model : x86_64 x86_64
% 0.15/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.43 % Memory : 8046.5625MB
% 0.15/5.43 % OS : Linux 6.8.0-71-generic
% 0.15/5.43 % CPULimit : 300
% 0.15/5.43 % WCLimit : 300
% 0.15/5.43 % DateTime : Mon Sep 21 05:56:39 UTC 2026
% 0.15/5.43 % CPUTime :
% 0.15/5.47 % Drodi V4.1.1
% 20.90/8.18 % Refutation found
% 20.90/8.18 % SZS status Theorem for theBenchmark: Theorem is valid
% 20.90/8.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.92/8.23 % Elapsed time: 2.773877 seconds
% 0.92/8.23 % CPU time: 21.587919 seconds
% 0.92/8.23 % Total memory used: 247.964 MB
% 0.92/8.23 % Net memory used: 226.615 MB
%------------------------------------------------------------------------------