%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU192+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 0.15s 5.55s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 70
% Syntax : Number of formulae : 310 ( 30 unt; 57 def)
% Number of atoms : 1085 ( 125 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 1303 ( 528 ~; 651 |; 47 &)
% ( 67 <=>; 9 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 62 ( 60 usr; 58 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 464 ( 440 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,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/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,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/sandbox/benchmark/theBenchmark.p') ).
fof(f31,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)],[f30]) ).
fof(f33,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f34,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f38,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)],[f4]) ).
fof(f39,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)],[f38]) ).
fof(f40,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)],[f39]) ).
fof(f41,plain,
! [A] :
( ! [C] :
( ( ! [B] :
( ( ( ( in(ordered_pair(sK0_skl(B,C,A),sK1_skl(B,C,A)),A)
& in(sK0_skl(B,C,A),B) )
| in(ordered_pair(sK0_skl(B,C,A),sK1_skl(B,C,A)),C) )
& ( ~ in(ordered_pair(sK0_skl(B,C,A),sK1_skl(B,C,A)),A)
| ~ in(sK0_skl(B,C,A),B)
| ~ in(ordered_pair(sK0_skl(B,C,A),sK1_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,[sK0_skl,sK1_skl]),skolemize(D,sK0_skl(B,C,A)),skolemize(E,sK1_skl(B,C,A))],[f40]) ).
fof(f42,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)],[f41]) ).
fof(f43,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)],[f41]) ).
fof(f44,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)],[f41]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(sK0_skl(X2,X1,X0),sK1_skl(X2,X1,X0)),X0)
| ~ in(sK0_skl(X2,X1,X0),X2)
| ~ in(ordered_pair(sK0_skl(X2,X1,X0),sK1_skl(X2,X1,X0)),X1)
| X1 = relation_dom_restriction(X0,X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f46,plain,
! [X0,X1,X2] :
( in(sK0_skl(X2,X1,X0),X2)
| in(ordered_pair(sK0_skl(X2,X1,X0),sK1_skl(X2,X1,X0)),X1)
| X1 = relation_dom_restriction(X0,X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f47,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK0_skl(X2,X1,X0),sK1_skl(X2,X1,X0)),X0)
| in(ordered_pair(sK0_skl(X2,X1,X0),sK1_skl(X2,X1,X0)),X1)
| X1 = relation_dom_restriction(X0,X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f48,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)],[f5]) ).
fof(f49,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)],[f48]) ).
fof(f50,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)],[f49]) ).
fof(f51,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK3_skl(B,A),sK4_skl(B,A)),A)
| in(sK3_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(sK3_skl(B,A),D),A)
| ~ in(sK3_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,sK2_skl(C,B,A)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(D,sK2_skl(C,B,A)),skolemize(C,sK3_skl(B,A)),skolemize(D,sK4_skl(B,A))],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( in(ordered_pair(X2,sK2_skl(X2,X1,X0)),X0)
| ~ in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,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)],[f51]) ).
fof(f55,plain,
! [X0,X1] :
( in(ordered_pair(sK3_skl(X1,X0),sK4_skl(X1,X0)),X0)
| in(sK3_skl(X1,X0),X1)
| X1 = relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f57,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f58,plain,
! [A] :
( ! [B] : relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f62,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f67,plain,
relation(empty_set),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f70,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f71,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f73,plain,
( relation(sK6_skl)
& empty(sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(A,sK6_skl)],[f22]) ).
fof(f74,plain,
empty(sK6_skl),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f75,plain,
relation(sK6_skl),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f76,plain,
empty(sK7_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(A,sK7_skl)],[f23]) ).
fof(f77,plain,
empty(sK7_skl),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
( relation(sK8_skl)
& ~ empty(sK8_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(A,sK8_skl)],[f24]) ).
fof(f80,plain,
relation(sK8_skl),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f87,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f88,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f89,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f90,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f92,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)],[f31]) ).
fof(f93,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)],[f92]) ).
fof(f94,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)],[f93]) ).
fof(f95,plain,
( ( ~ in(sK11_skl,relation_dom(sK10_skl))
| ~ in(sK11_skl,sK12_skl)
| ~ in(sK11_skl,relation_dom(relation_dom_restriction(sK10_skl,sK12_skl))) )
& ( ( in(sK11_skl,relation_dom(sK10_skl))
& in(sK11_skl,sK12_skl) )
| in(sK11_skl,relation_dom(relation_dom_restriction(sK10_skl,sK12_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)],[f94]) ).
fof(f96,plain,
relation(sK10_skl),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f97,plain,
( in(sK11_skl,sK12_skl)
| in(sK11_skl,relation_dom(relation_dom_restriction(sK10_skl,sK12_skl))) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f98,plain,
( in(sK11_skl,relation_dom(sK10_skl))
| in(sK11_skl,relation_dom(relation_dom_restriction(sK10_skl,sK12_skl))) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f99,plain,
( ~ in(sK11_skl,relation_dom(sK10_skl))
| ~ in(sK11_skl,sK12_skl)
| ~ in(sK11_skl,relation_dom(relation_dom_restriction(sK10_skl,sK12_skl))) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f103,definition,
( sQ0_spl
<=> in(sK11_skl,relation_dom(relation_dom_restriction(sK10_skl,sK12_skl))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( ~ sQ0_spl
| in(sK11_skl,relation_dom(relation_dom_restriction(sK10_skl,sK12_skl))) ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f105,plain,
( sQ0_spl
| ~ in(sK11_skl,relation_dom(relation_dom_restriction(sK10_skl,sK12_skl))) ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,definition,
( sQ1_spl
<=> in(sK11_skl,sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f109,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f97,f103,f106]) ).
fof(f110,definition,
( sQ2_spl
<=> in(sK11_skl,relation_dom(sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f113,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f98,f103,f110]) ).
fof(f114,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f99,f103,f106,f110]) ).
fof(f115,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)],[f42]) ).
fof(f116,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)],[f43]) ).
fof(f117,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)],[f44]) ).
fof(f118,plain,
! [X0,X1] :
( in(ordered_pair(X1,sK2_skl(X1,relation_dom(X0),X0)),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f52]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f53]) ).
fof(f128,plain,
! [X0,X1] :
( in(ordered_pair(sK0_skl(X1,sK6_skl,X0),sK1_skl(X1,sK6_skl,X0)),X0)
| in(ordered_pair(sK0_skl(X1,sK6_skl,X0),sK1_skl(X1,sK6_skl,X0)),sK6_skl)
| sK6_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f47,f75]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ~ empty(X1)
| in(ordered_pair(sK0_skl(X2,relation_dom(X1),X0),sK1_skl(X2,relation_dom(X1),X0)),X0)
| in(ordered_pair(sK0_skl(X2,relation_dom(X1),X0),sK1_skl(X2,relation_dom(X1),X0)),relation_dom(X1))
| relation_dom(X1) = relation_dom_restriction(X0,X2)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f47,f72]) ).
fof(f130,plain,
! [X0,X1] :
( in(ordered_pair(sK0_skl(X1,sK10_skl,X0),sK1_skl(X1,sK10_skl,X0)),X0)
| in(ordered_pair(sK0_skl(X1,sK10_skl,X0),sK1_skl(X1,sK10_skl,X0)),sK10_skl)
| sK10_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f47,f96]) ).
fof(f132,plain,
! [X0,X1] :
( ~ in(X0,ordered_pair(X1,sK2_skl(X1,relation_dom(X0),X0)))
| ~ in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f118,f34]) ).
fof(f133,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK0_skl(X1,sK10_skl,X0),sK1_skl(X1,sK10_skl,X0)),X0)
| ~ in(sK0_skl(X1,sK10_skl,X0),X1)
| sK10_skl = relation_dom_restriction(X0,X1)
| ~ relation(sK10_skl)
| ~ relation(X0)
| in(ordered_pair(sK0_skl(X1,sK10_skl,X0),sK1_skl(X1,sK10_skl,X0)),X0)
| sK10_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f130,f45]) ).
fof(f134,plain,
! [X0,X1] :
( in(sK0_skl(X1,sK10_skl,X0),relation_dom(sK10_skl))
| ~ relation(sK10_skl)
| in(ordered_pair(sK0_skl(X1,sK10_skl,X0),sK1_skl(X1,sK10_skl,X0)),X0)
| sK10_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f130,f119]) ).
fof(f136,definition,
! [X0,X1] :
( sQ3_spl
<=> ( ~ in(ordered_pair(sK0_skl(X1,sK10_skl,X0),sK1_skl(X1,sK10_skl,X0)),X0)
| ~ in(sK0_skl(X1,sK10_skl,X0),X1)
| sK10_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0)
| in(ordered_pair(sK0_skl(X1,sK10_skl,X0),sK1_skl(X1,sK10_skl,X0)),X0)
| sK10_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f139,definition,
( sQ4_spl
<=> relation(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f141,plain,
( sQ4_spl
| ~ relation(sK10_skl) ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( ~ sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f133,f136,f139]) ).
fof(f143,definition,
! [X0,X1] :
( sQ5_spl
<=> ( in(sK0_skl(X1,sK10_skl,X0),relation_dom(sK10_skl))
| in(ordered_pair(sK0_skl(X1,sK10_skl,X0),sK1_skl(X1,sK10_skl,X0)),X0)
| sK10_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f144,plain,
! [X0,X1] :
( ~ sQ5_spl
| in(sK0_skl(X1,sK10_skl,X0),relation_dom(sK10_skl))
| in(ordered_pair(sK0_skl(X1,sK10_skl,X0),sK1_skl(X1,sK10_skl,X0)),X0)
| sK10_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,plain,
( ~ sQ4_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f134,f143,f139]) ).
fof(f147,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f141,f96]) ).
fof(f148,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f147]) ).
fof(f149,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(backward_subsumption_resolution,[status(thm)],[f117,f59]) ).
fof(f150,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)],[f116,f59]) ).
fof(f151,plain,
! [X0,X1,X2,X3] :
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),relation_dom_restriction(X0,X3))
| ~ relation(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f115,f59]) ).
fof(f153,plain,
! [X0,X1] :
( ~ empty(X0)
| relation(relation_dom_restriction(relation_dom(X0),X1)) ),
inference(resolution,[status(thm)],[f59,f72]) ).
fof(f154,plain,
! [X0] : relation(relation_dom_restriction(sK10_skl,X0)),
inference(resolution,[status(thm)],[f59,f96]) ).
fof(f159,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK0_skl(X0,sK10_skl,X1),sK1_skl(X0,sK10_skl,X1)),X1)
| sK10_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| ~ in(sK0_skl(X0,sK10_skl,X1),X2)
| in(ordered_pair(sK0_skl(X0,sK10_skl,X1),sK1_skl(X0,sK10_skl,X1)),relation_dom_restriction(sK10_skl,X2))
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f149,f130]) ).
fof(f160,plain,
! [X0,X1,X2] :
( ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ in(X1,X2)
| in(ordered_pair(X1,sK2_skl(X1,relation_dom(X0),X0)),relation_dom_restriction(X0,X2))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f149,f118]) ).
fof(f161,definition,
! [X0,X1,X2] :
( sQ6_spl
<=> ( in(ordered_pair(sK0_skl(X0,sK10_skl,X1),sK1_skl(X0,sK10_skl,X1)),X1)
| sK10_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| ~ in(sK0_skl(X0,sK10_skl,X1),X2)
| in(ordered_pair(sK0_skl(X0,sK10_skl,X1),sK1_skl(X0,sK10_skl,X1)),relation_dom_restriction(sK10_skl,X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f162,plain,
! [X0,X1,X2] :
( ~ sQ6_spl
| in(ordered_pair(sK0_skl(X0,sK10_skl,X1),sK1_skl(X0,sK10_skl,X1)),X1)
| sK10_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| ~ in(sK0_skl(X0,sK10_skl,X1),X2)
| in(ordered_pair(sK0_skl(X0,sK10_skl,X1),sK1_skl(X0,sK10_skl,X1)),relation_dom_restriction(sK10_skl,X2)) ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f164,plain,
( sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f159,f139,f161]) ).
fof(f165,plain,
! [X0,X1,X2] :
( ~ in(X1,relation_dom(X0))
| ~ in(X1,X2)
| in(ordered_pair(X1,sK2_skl(X1,relation_dom(X0),X0)),relation_dom_restriction(X0,X2))
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f160]) ).
fof(f166,plain,
! [X0,X1,X2] :
( ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ relation(relation_dom_restriction(X0,X2))
| in(ordered_pair(X1,sK2_skl(X1,relation_dom(relation_dom_restriction(X0,X2)),relation_dom_restriction(X0,X2))),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f150,f118]) ).
fof(f167,plain,
! [X0,X1,X2] :
( ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| in(ordered_pair(X1,sK2_skl(X1,relation_dom(relation_dom_restriction(X0,X2)),relation_dom_restriction(X0,X2))),X0)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f166,f59]) ).
fof(f168,plain,
! [X0] : relation(relation_dom_restriction(sK8_skl,X0)),
inference(resolution,[status(thm)],[f80,f59]) ).
fof(f169,plain,
! [X0,X1] :
( in(ordered_pair(sK0_skl(X1,sK8_skl,X0),sK1_skl(X1,sK8_skl,X0)),X0)
| in(ordered_pair(sK0_skl(X1,sK8_skl,X0),sK1_skl(X1,sK8_skl,X0)),sK8_skl)
| sK8_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f80,f47]) ).
fof(f182,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK10_skl,X1),X0),sK1_skl(X2,relation_dom_restriction(sK10_skl,X1),X0)),X0)
| in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK10_skl,X1),X0),sK1_skl(X2,relation_dom_restriction(sK10_skl,X1),X0)),relation_dom_restriction(sK10_skl,X1))
| relation_dom_restriction(sK10_skl,X1) = relation_dom_restriction(X0,X2)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f154,f47]) ).
fof(f184,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ6_spl
| in(ordered_pair(sK0_skl(X0,sK10_skl,X1),sK1_skl(X0,sK10_skl,X1)),X1)
| sK10_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| in(ordered_pair(sK0_skl(X0,sK10_skl,X1),sK1_skl(X0,sK10_skl,X1)),X1)
| sK10_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| in(ordered_pair(sK0_skl(X0,sK10_skl,X1),sK1_skl(X0,sK10_skl,X1)),relation_dom_restriction(sK10_skl,relation_dom(sK10_skl))) ),
inference(resolution,[status(thm)],[f162,f144]) ).
fof(f185,plain,
! [X0,X1] :
( ~ sQ6_spl
| in(ordered_pair(sK0_skl(X0,sK10_skl,X1),sK1_skl(X0,sK10_skl,X1)),sK10_skl)
| sK10_skl = relation_dom_restriction(X1,X0)
| ~ relation(sK10_skl)
| ~ relation(X1)
| in(ordered_pair(sK0_skl(X0,sK10_skl,X1),sK1_skl(X0,sK10_skl,X1)),X1)
| sK10_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| in(ordered_pair(sK0_skl(X0,sK10_skl,X1),sK1_skl(X0,sK10_skl,X1)),relation_dom_restriction(sK10_skl,X0)) ),
inference(resolution,[status(thm)],[f162,f46]) ).
fof(f186,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ6_spl
| in(ordered_pair(sK0_skl(X0,sK10_skl,X1),sK1_skl(X0,sK10_skl,X1)),X1)
| sK10_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| in(ordered_pair(sK0_skl(X0,sK10_skl,X1),sK1_skl(X0,sK10_skl,X1)),relation_dom_restriction(sK10_skl,relation_dom(sK10_skl))) ),
inference(duplicate_literals_removal,[status(thm)],[f184]) ).
fof(f187,definition,
! [X0,X1] :
( sQ7_spl
<=> ( in(ordered_pair(sK0_skl(X0,sK10_skl,X1),sK1_skl(X0,sK10_skl,X1)),sK10_skl)
| sK10_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| in(ordered_pair(sK0_skl(X0,sK10_skl,X1),sK1_skl(X0,sK10_skl,X1)),X1)
| sK10_skl = relation_dom_restriction(X1,X0)
| ~ relation(X1)
| in(ordered_pair(sK0_skl(X0,sK10_skl,X1),sK1_skl(X0,sK10_skl,X1)),relation_dom_restriction(sK10_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f185,f187,f139,f161]) ).
fof(f193,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK8_skl,X1),X0),sK1_skl(X2,relation_dom_restriction(sK8_skl,X1),X0)),X0)
| in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK8_skl,X1),X0),sK1_skl(X2,relation_dom_restriction(sK8_skl,X1),X0)),relation_dom_restriction(sK8_skl,X1))
| relation_dom_restriction(sK8_skl,X1) = relation_dom_restriction(X0,X2)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f168,f47]) ).
fof(f196,plain,
! [X0,X1,X2] :
( ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ relation(relation_dom_restriction(X0,X2))
| in(X1,X2)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f151,f118]) ).
fof(f197,plain,
! [X0,X1,X2] :
( ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| in(X1,X2)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f196,f59]) ).
fof(f206,plain,
! [X0] : ~ in(X0,empty_set),
inference(resolution,[status(thm)],[f91,f62]) ).
fof(f207,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,relation_dom(X1)) ),
inference(resolution,[status(thm)],[f91,f71]) ).
fof(f210,plain,
! [X0] :
( in(ordered_pair(sK3_skl(empty_set,X0),sK4_skl(empty_set,X0)),X0)
| empty_set = relation_dom(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f206,f55]) ).
fof(f211,plain,
! [X0] :
( ~ in(X0,relation_dom(empty_set))
| ~ relation(empty_set) ),
inference(resolution,[status(thm)],[f206,f118]) ).
fof(f212,plain,
! [X0,X1] :
( in(ordered_pair(sK0_skl(empty_set,X1,X0),sK1_skl(empty_set,X1,X0)),X1)
| X1 = relation_dom_restriction(X0,empty_set)
| ~ relation(X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f206,f46]) ).
fof(f213,definition,
( sQ8_spl
<=> relation(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f215,plain,
( sQ8_spl
| ~ relation(empty_set) ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f216,definition,
! [X0] :
( sQ9_spl
<=> ~ in(X0,relation_dom(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f217,plain,
! [X0] :
( ~ sQ9_spl
| ~ in(X0,relation_dom(empty_set)) ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f219,plain,
( sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f211,f213,f216]) ).
fof(f224,plain,
! [X0,X1] :
( in(ordered_pair(sK0_skl(X1,empty_set,X0),sK1_skl(X1,empty_set,X0)),X0)
| in(ordered_pair(sK0_skl(X1,empty_set,X0),sK1_skl(X1,empty_set,X0)),empty_set)
| empty_set = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f67,f47]) ).
fof(f225,plain,
! [X0,X1] :
( in(ordered_pair(sK0_skl(X1,empty_set,X0),sK1_skl(X1,empty_set,X0)),X0)
| empty_set = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f224,f206]) ).
fof(f231,plain,
! [X0,X1,X2] :
( in(sK0_skl(X2,relation_dom_restriction(sK10_skl,X1),X0),X1)
| ~ relation(sK10_skl)
| in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK10_skl,X1),X0),sK1_skl(X2,relation_dom_restriction(sK10_skl,X1),X0)),X0)
| relation_dom_restriction(sK10_skl,X1) = relation_dom_restriction(X0,X2)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f182,f151]) ).
fof(f232,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK10_skl,X1),X0),sK1_skl(X2,relation_dom_restriction(sK10_skl,X1),X0)),sK10_skl)
| ~ relation(sK10_skl)
| in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK10_skl,X1),X0),sK1_skl(X2,relation_dom_restriction(sK10_skl,X1),X0)),X0)
| relation_dom_restriction(sK10_skl,X1) = relation_dom_restriction(X0,X2)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f182,f150]) ).
fof(f234,plain,
! [X0,X1,X2] :
( in(sK0_skl(X2,relation_dom_restriction(sK10_skl,X1),X0),relation_dom(relation_dom_restriction(sK10_skl,X1)))
| ~ relation(relation_dom_restriction(sK10_skl,X1))
| in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK10_skl,X1),X0),sK1_skl(X2,relation_dom_restriction(sK10_skl,X1),X0)),X0)
| relation_dom_restriction(sK10_skl,X1) = relation_dom_restriction(X0,X2)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f182,f119]) ).
fof(f236,definition,
! [X0,X1,X2] :
( sQ10_spl
<=> ( in(sK0_skl(X2,relation_dom_restriction(sK10_skl,X1),X0),X1)
| in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK10_skl,X1),X0),sK1_skl(X2,relation_dom_restriction(sK10_skl,X1),X0)),X0)
| relation_dom_restriction(sK10_skl,X1) = relation_dom_restriction(X0,X2)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f239,plain,
( ~ sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f231,f236,f139]) ).
fof(f240,definition,
! [X0,X1,X2] :
( sQ11_spl
<=> ( in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK10_skl,X1),X0),sK1_skl(X2,relation_dom_restriction(sK10_skl,X1),X0)),sK10_skl)
| in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK10_skl,X1),X0),sK1_skl(X2,relation_dom_restriction(sK10_skl,X1),X0)),X0)
| relation_dom_restriction(sK10_skl,X1) = relation_dom_restriction(X0,X2)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( ~ sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f232,f240,f139]) ).
fof(f245,plain,
! [X0,X1,X2] :
( in(sK0_skl(X2,relation_dom_restriction(sK10_skl,X1),X0),relation_dom(relation_dom_restriction(sK10_skl,X1)))
| in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK10_skl,X1),X0),sK1_skl(X2,relation_dom_restriction(sK10_skl,X1),X0)),X0)
| relation_dom_restriction(sK10_skl,X1) = relation_dom_restriction(X0,X2)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f234,f154]) ).
fof(f254,plain,
! [X0,X1,X2,X3] :
( ~ in(X1,X3)
| in(ordered_pair(X1,sK2_skl(X1,relation_dom(X0),X0)),relation_dom_restriction(relation_dom_restriction(X0,X2),X3))
| ~ relation(relation_dom_restriction(X0,X2))
| ~ in(X1,relation_dom(X0))
| ~ in(X1,X2)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f165,f149]) ).
fof(f255,plain,
! [X0,X1,X2] :
( in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ relation(relation_dom_restriction(X0,X2))
| ~ in(X1,relation_dom(X0))
| ~ in(X1,X2)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f165,f119]) ).
fof(f256,plain,
! [X0,X1,X2] :
( ~ in(relation_dom_restriction(X0,X2),ordered_pair(X1,sK2_skl(X1,relation_dom(X0),X0)))
| ~ in(X1,relation_dom(X0))
| ~ in(X1,X2)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f165,f34]) ).
fof(f258,plain,
! [X0,X1,X2,X3] :
( ~ in(X1,X3)
| in(ordered_pair(X1,sK2_skl(X1,relation_dom(X0),X0)),relation_dom_restriction(relation_dom_restriction(X0,X2),X3))
| ~ in(X1,relation_dom(X0))
| ~ in(X1,X2)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f254,f59]) ).
fof(f259,plain,
! [X0,X1,X2] :
( in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ in(X1,relation_dom(X0))
| ~ in(X1,X2)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f255,f59]) ).
fof(f260,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK3_skl(relation_dom(relation_dom_restriction(X0,X1)),X2),sK4_skl(relation_dom(relation_dom_restriction(X0,X1)),X2)),X2)
| relation_dom(relation_dom_restriction(X0,X1)) = relation_dom(X2)
| ~ relation(X2)
| in(ordered_pair(sK3_skl(relation_dom(relation_dom_restriction(X0,X1)),X2),sK2_skl(sK3_skl(relation_dom(relation_dom_restriction(X0,X1)),X2),relation_dom(relation_dom_restriction(X0,X1)),relation_dom_restriction(X0,X1))),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f167,f55]) ).
fof(f264,plain,
( ~ sQ0_spl
| in(ordered_pair(sK11_skl,sK2_skl(sK11_skl,relation_dom(relation_dom_restriction(sK10_skl,sK12_skl)),relation_dom_restriction(sK10_skl,sK12_skl))),sK10_skl)
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f167,f104]) ).
fof(f265,definition,
( sQ12_spl
<=> in(ordered_pair(sK11_skl,sK2_skl(sK11_skl,relation_dom(relation_dom_restriction(sK10_skl,sK12_skl)),relation_dom_restriction(sK10_skl,sK12_skl))),sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f266,plain,
( ~ sQ12_spl
| in(ordered_pair(sK11_skl,sK2_skl(sK11_skl,relation_dom(relation_dom_restriction(sK10_skl,sK12_skl)),relation_dom_restriction(sK10_skl,sK12_skl))),sK10_skl) ),
inference(component_clause,[status(thm)],[f265]) ).
fof(f268,plain,
( ~ sQ0_spl
| sQ12_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f264,f139,f265,f103]) ).
fof(f269,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f215,f67]) ).
fof(f270,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f269]) ).
fof(f272,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ empty(empty_set)
| in(ordered_pair(sK0_skl(X1,relation_dom(empty_set),X0),sK1_skl(X1,relation_dom(empty_set),X0)),X0)
| relation_dom(empty_set) = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f217,f129]) ).
fof(f273,plain,
! [X0] :
( ~ sQ9_spl
| ~ in(X0,relation_dom(relation_dom(empty_set)))
| ~ relation(relation_dom(empty_set)) ),
inference(resolution,[status(thm)],[f217,f118]) ).
fof(f275,definition,
! [X0,X1] :
( sQ13_spl
<=> ( in(ordered_pair(sK0_skl(X1,relation_dom(empty_set),X0),sK1_skl(X1,relation_dom(empty_set),X0)),X0)
| relation_dom(empty_set) = relation_dom_restriction(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f278,definition,
( sQ14_spl
<=> empty(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f281,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f272,f275,f278,f216]) ).
fof(f282,definition,
( sQ15_spl
<=> relation(relation_dom(empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f284,plain,
( sQ15_spl
| ~ relation(relation_dom(empty_set)) ),
inference(component_clause,[status(thm)],[f282]) ).
fof(f285,definition,
! [X0] :
( sQ16_spl
<=> ~ in(X0,relation_dom(relation_dom(empty_set))) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f288,plain,
( ~ sQ9_spl
| sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f273,f282,f285,f216]) ).
fof(f290,plain,
! [X0] :
( ~ empty(X0)
| relation_dom(X0) = empty_set ),
inference(resolution,[status(thm)],[f88,f71]) ).
fof(f291,plain,
sK7_skl = empty_set,
inference(resolution,[status(thm)],[f88,f77]) ).
fof(f292,plain,
sK6_skl = empty_set,
inference(resolution,[status(thm)],[f88,f74]) ).
fof(f297,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK0_skl(X1,sK6_skl,X0),sK1_skl(X1,sK6_skl,X0)),X0)
| ~ in(sK0_skl(X1,sK6_skl,X0),X1)
| sK6_skl = relation_dom_restriction(X0,X1)
| ~ relation(sK6_skl)
| ~ relation(X0)
| in(ordered_pair(sK0_skl(X1,sK6_skl,X0),sK1_skl(X1,sK6_skl,X0)),X0)
| sK6_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f128,f45]) ).
fof(f298,plain,
! [X0,X1,X2] :
( ~ in(sK0_skl(X1,sK6_skl,X0),X2)
| in(ordered_pair(sK0_skl(X1,sK6_skl,X0),sK1_skl(X1,sK6_skl,X0)),relation_dom_restriction(sK6_skl,X2))
| ~ relation(sK6_skl)
| in(ordered_pair(sK0_skl(X1,sK6_skl,X0),sK1_skl(X1,sK6_skl,X0)),X0)
| sK6_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f128,f149]) ).
fof(f299,plain,
! [X0,X1] :
( in(sK0_skl(X1,sK6_skl,X0),relation_dom(sK6_skl))
| ~ relation(sK6_skl)
| in(ordered_pair(sK0_skl(X1,sK6_skl,X0),sK1_skl(X1,sK6_skl,X0)),X0)
| sK6_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f128,f119]) ).
fof(f301,definition,
! [X0,X1] :
( sQ17_spl
<=> ( ~ in(ordered_pair(sK0_skl(X1,sK6_skl,X0),sK1_skl(X1,sK6_skl,X0)),X0)
| ~ in(sK0_skl(X1,sK6_skl,X0),X1)
| sK6_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0)
| in(ordered_pair(sK0_skl(X1,sK6_skl,X0),sK1_skl(X1,sK6_skl,X0)),X0)
| sK6_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f304,definition,
( sQ18_spl
<=> relation(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f306,plain,
( sQ18_spl
| ~ relation(sK6_skl) ),
inference(component_clause,[status(thm)],[f304]) ).
fof(f307,plain,
( ~ sQ18_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f297,f301,f304]) ).
fof(f308,definition,
! [X0,X1,X2] :
( sQ19_spl
<=> ( ~ in(sK0_skl(X1,sK6_skl,X0),X2)
| in(ordered_pair(sK0_skl(X1,sK6_skl,X0),sK1_skl(X1,sK6_skl,X0)),relation_dom_restriction(sK6_skl,X2))
| in(ordered_pair(sK0_skl(X1,sK6_skl,X0),sK1_skl(X1,sK6_skl,X0)),X0)
| sK6_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f311,plain,
( ~ sQ18_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f298,f308,f304]) ).
fof(f312,definition,
! [X0,X1] :
( sQ20_spl
<=> ( in(sK0_skl(X1,sK6_skl,X0),relation_dom(sK6_skl))
| in(ordered_pair(sK0_skl(X1,sK6_skl,X0),sK1_skl(X1,sK6_skl,X0)),X0)
| sK6_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f315,plain,
( ~ sQ18_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f299,f312,f304]) ).
fof(f316,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f306,f75]) ).
fof(f317,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f316]) ).
fof(f318,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK0_skl(X1,sK8_skl,X0),sK1_skl(X1,sK8_skl,X0)),X0)
| ~ in(sK0_skl(X1,sK8_skl,X0),X1)
| sK8_skl = relation_dom_restriction(X0,X1)
| ~ relation(sK8_skl)
| ~ relation(X0)
| in(ordered_pair(sK0_skl(X1,sK8_skl,X0),sK1_skl(X1,sK8_skl,X0)),X0)
| sK8_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f169,f45]) ).
fof(f319,plain,
! [X0,X1,X2] :
( ~ in(sK0_skl(X1,sK8_skl,X0),X2)
| in(ordered_pair(sK0_skl(X1,sK8_skl,X0),sK1_skl(X1,sK8_skl,X0)),relation_dom_restriction(sK8_skl,X2))
| ~ relation(sK8_skl)
| in(ordered_pair(sK0_skl(X1,sK8_skl,X0),sK1_skl(X1,sK8_skl,X0)),X0)
| sK8_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f169,f149]) ).
fof(f320,plain,
! [X0,X1] :
( in(sK0_skl(X1,sK8_skl,X0),relation_dom(sK8_skl))
| ~ relation(sK8_skl)
| in(ordered_pair(sK0_skl(X1,sK8_skl,X0),sK1_skl(X1,sK8_skl,X0)),X0)
| sK8_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f169,f119]) ).
fof(f322,definition,
! [X0,X1] :
( sQ21_spl
<=> ( ~ in(ordered_pair(sK0_skl(X1,sK8_skl,X0),sK1_skl(X1,sK8_skl,X0)),X0)
| ~ in(sK0_skl(X1,sK8_skl,X0),X1)
| sK8_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0)
| in(ordered_pair(sK0_skl(X1,sK8_skl,X0),sK1_skl(X1,sK8_skl,X0)),X0)
| sK8_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f325,definition,
( sQ22_spl
<=> relation(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f327,plain,
( sQ22_spl
| ~ relation(sK8_skl) ),
inference(component_clause,[status(thm)],[f325]) ).
fof(f328,plain,
( ~ sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f318,f322,f325]) ).
fof(f329,definition,
! [X0,X1,X2] :
( sQ23_spl
<=> ( ~ in(sK0_skl(X1,sK8_skl,X0),X2)
| in(ordered_pair(sK0_skl(X1,sK8_skl,X0),sK1_skl(X1,sK8_skl,X0)),relation_dom_restriction(sK8_skl,X2))
| in(ordered_pair(sK0_skl(X1,sK8_skl,X0),sK1_skl(X1,sK8_skl,X0)),X0)
| sK8_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f332,plain,
( ~ sQ22_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f319,f329,f325]) ).
fof(f333,definition,
! [X0,X1] :
( sQ24_spl
<=> ( in(sK0_skl(X1,sK8_skl,X0),relation_dom(sK8_skl))
| in(ordered_pair(sK0_skl(X1,sK8_skl,X0),sK1_skl(X1,sK8_skl,X0)),X0)
| sK8_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f336,plain,
( ~ sQ22_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f320,f333,f325]) ).
fof(f337,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f327,f80]) ).
fof(f338,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f337]) ).
fof(f351,plain,
! [X0] :
( ~ sQ12_spl
| ~ in(sK11_skl,X0)
| in(ordered_pair(sK11_skl,sK2_skl(sK11_skl,relation_dom(relation_dom_restriction(sK10_skl,sK12_skl)),relation_dom_restriction(sK10_skl,sK12_skl))),relation_dom_restriction(sK10_skl,X0))
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f266,f149]) ).
fof(f352,plain,
( ~ sQ12_spl
| in(sK11_skl,relation_dom(sK10_skl))
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f266,f119]) ).
fof(f354,definition,
! [X0] :
( sQ25_spl
<=> ( ~ in(sK11_skl,X0)
| in(ordered_pair(sK11_skl,sK2_skl(sK11_skl,relation_dom(relation_dom_restriction(sK10_skl,sK12_skl)),relation_dom_restriction(sK10_skl,sK12_skl))),relation_dom_restriction(sK10_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f357,plain,
( ~ sQ12_spl
| sQ25_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f351,f139,f354,f265]) ).
fof(f358,plain,
( ~ sQ12_spl
| sQ2_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f352,f139,f110,f265]) ).
fof(f368,plain,
! [X0] : ~ in(X0,relation_dom(sK7_skl)),
inference(resolution,[status(thm)],[f207,f77]) ).
fof(f372,plain,
relation_dom(sK7_skl) = empty_set,
inference(resolution,[status(thm)],[f290,f77]) ).
fof(f381,plain,
sK7_skl = sK6_skl,
inference(backward_demodulation,[status(thm)],[f292,f291]) ).
fof(f417,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ6_spl
| in(ordered_pair(sK0_skl(X1,sK10_skl,X0),sK1_skl(X1,sK10_skl,X0)),sK10_skl)
| ~ relation(sK10_skl)
| in(ordered_pair(sK0_skl(X1,sK10_skl,X0),sK1_skl(X1,sK10_skl,X0)),X0)
| sK10_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f186,f150]) ).
fof(f418,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ in(sK0_skl(X1,sK10_skl,X0),X2)
| in(ordered_pair(sK0_skl(X1,sK10_skl,X0),sK1_skl(X1,sK10_skl,X0)),relation_dom_restriction(relation_dom_restriction(sK10_skl,relation_dom(sK10_skl)),X2))
| ~ relation(relation_dom_restriction(sK10_skl,relation_dom(sK10_skl)))
| in(ordered_pair(sK0_skl(X1,sK10_skl,X0),sK1_skl(X1,sK10_skl,X0)),X0)
| sK10_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f186,f149]) ).
fof(f419,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ6_spl
| in(sK0_skl(X1,sK10_skl,X0),relation_dom(relation_dom_restriction(sK10_skl,relation_dom(sK10_skl))))
| ~ relation(relation_dom_restriction(sK10_skl,relation_dom(sK10_skl)))
| in(ordered_pair(sK0_skl(X1,sK10_skl,X0),sK1_skl(X1,sK10_skl,X0)),X0)
| sK10_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f186,f119]) ).
fof(f422,definition,
! [X0,X1] :
( sQ26_spl
<=> ( in(ordered_pair(sK0_skl(X1,sK10_skl,X0),sK1_skl(X1,sK10_skl,X0)),sK10_skl)
| in(ordered_pair(sK0_skl(X1,sK10_skl,X0),sK1_skl(X1,sK10_skl,X0)),X0)
| sK10_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f425,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f417,f422,f139,f161,f143]) ).
fof(f426,definition,
! [X0,X1,X2] :
( sQ27_spl
<=> ( ~ in(sK0_skl(X1,sK10_skl,X0),X2)
| in(ordered_pair(sK0_skl(X1,sK10_skl,X0),sK1_skl(X1,sK10_skl,X0)),relation_dom_restriction(relation_dom_restriction(sK10_skl,relation_dom(sK10_skl)),X2))
| in(ordered_pair(sK0_skl(X1,sK10_skl,X0),sK1_skl(X1,sK10_skl,X0)),X0)
| sK10_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f429,definition,
( sQ28_spl
<=> relation(relation_dom_restriction(sK10_skl,relation_dom(sK10_skl))) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f431,plain,
( sQ28_spl
| ~ relation(relation_dom_restriction(sK10_skl,relation_dom(sK10_skl))) ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f432,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ28_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f418,f426,f429,f161,f143]) ).
fof(f433,definition,
! [X0,X1] :
( sQ29_spl
<=> ( in(sK0_skl(X1,sK10_skl,X0),relation_dom(relation_dom_restriction(sK10_skl,relation_dom(sK10_skl))))
| in(ordered_pair(sK0_skl(X1,sK10_skl,X0),sK1_skl(X1,sK10_skl,X0)),X0)
| sK10_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f436,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ28_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f419,f433,f429,f161,f143]) ).
fof(f437,plain,
( sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f431,f154]) ).
fof(f438,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f437]) ).
fof(f449,plain,
relation_dom(sK6_skl) = empty_set,
inference(forward_demodulation,[status(thm)],[f381,f372]) ).
fof(f450,plain,
relation_dom(sK6_skl) = sK6_skl,
inference(forward_demodulation,[status(thm)],[f292,f449]) ).
fof(f451,plain,
! [X0,X1] :
( ~ in(X0,relation_dom(sK6_skl))
| ~ in(X0,X1)
| in(ordered_pair(X0,sK2_skl(X0,sK6_skl,sK6_skl)),relation_dom_restriction(sK6_skl,X1))
| ~ relation(sK6_skl) ),
inference(paramodulation,[status(thm)],[f450,f165]) ).
fof(f452,plain,
! [X0] :
( ~ empty(sK6_skl)
| relation(relation_dom_restriction(sK6_skl,X0)) ),
inference(paramodulation,[status(thm)],[f450,f153]) ).
fof(f453,plain,
! [X0] :
( ~ in(sK6_skl,ordered_pair(X0,sK2_skl(X0,sK6_skl,sK6_skl)))
| ~ in(X0,relation_dom(sK6_skl))
| ~ relation(sK6_skl) ),
inference(paramodulation,[status(thm)],[f450,f132]) ).
fof(f456,plain,
! [X0] :
( in(ordered_pair(X0,sK2_skl(X0,sK6_skl,sK6_skl)),sK6_skl)
| ~ in(X0,relation_dom(sK6_skl))
| ~ relation(sK6_skl) ),
inference(paramodulation,[status(thm)],[f450,f118]) ).
fof(f458,definition,
! [X0,X1] :
( sQ30_spl
<=> ( ~ in(X0,relation_dom(sK6_skl))
| ~ in(X0,X1)
| in(ordered_pair(X0,sK2_skl(X0,sK6_skl,sK6_skl)),relation_dom_restriction(sK6_skl,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f461,plain,
( sQ30_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f451,f304,f458]) ).
fof(f462,definition,
! [X0] :
( sQ31_spl
<=> relation(relation_dom_restriction(sK6_skl,X0)) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f465,definition,
( sQ32_spl
<=> empty(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f467,plain,
( sQ32_spl
| ~ empty(sK6_skl) ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f468,plain,
( ~ sQ32_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f452,f462,f465]) ).
fof(f469,definition,
! [X0] :
( sQ33_spl
<=> ( ~ in(sK6_skl,ordered_pair(X0,sK2_skl(X0,sK6_skl,sK6_skl)))
| ~ in(X0,relation_dom(sK6_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f472,plain,
( sQ33_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f453,f304,f469]) ).
fof(f475,definition,
! [X0] :
( sQ34_spl
<=> ( in(ordered_pair(X0,sK2_skl(X0,sK6_skl,sK6_skl)),sK6_skl)
| ~ in(X0,relation_dom(sK6_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f478,plain,
( sQ34_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f456,f304,f475]) ).
fof(f480,plain,
( sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f467,f74]) ).
fof(f481,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f480]) ).
fof(f497,plain,
! [X0] : ~ in(X0,relation_dom(sK6_skl)),
inference(forward_demodulation,[status(thm)],[f381,f368]) ).
fof(f499,plain,
! [X0] : ~ in(X0,sK6_skl),
inference(forward_demodulation,[status(thm)],[f450,f497]) ).
fof(f501,plain,
! [X0] :
( ~ in(X0,relation_dom(sK6_skl))
| ~ relation(sK6_skl) ),
inference(resolution,[status(thm)],[f499,f118]) ).
fof(f503,definition,
! [X0] :
( sQ35_spl
<=> ~ in(X0,relation_dom(sK6_skl)) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f506,plain,
( sQ35_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f501,f304,f503]) ).
fof(f512,plain,
! [X0,X1] :
( in(ordered_pair(sK0_skl(X1,empty_set,X0),sK1_skl(X1,empty_set,X0)),X0)
| sK6_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f292,f225]) ).
fof(f513,plain,
! [X0,X1] :
( in(ordered_pair(sK0_skl(X1,sK6_skl,X0),sK1_skl(X1,empty_set,X0)),X0)
| sK6_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f292,f512]) ).
fof(f514,plain,
! [X0,X1] :
( in(ordered_pair(sK0_skl(X1,sK6_skl,X0),sK1_skl(X1,sK6_skl,X0)),X0)
| sK6_skl = relation_dom_restriction(X0,X1)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f292,f513]) ).
fof(f515,plain,
! [X0] :
( ~ in(ordered_pair(sK0_skl(X0,sK6_skl,sK6_skl),sK1_skl(X0,sK6_skl,sK6_skl)),sK6_skl)
| ~ in(sK0_skl(X0,sK6_skl,sK6_skl),X0)
| sK6_skl = relation_dom_restriction(sK6_skl,X0)
| ~ relation(sK6_skl)
| ~ relation(sK6_skl)
| sK6_skl = relation_dom_restriction(sK6_skl,X0)
| ~ relation(sK6_skl) ),
inference(resolution,[status(thm)],[f514,f45]) ).
fof(f520,plain,
! [X0] :
( sK6_skl = relation_dom_restriction(sK6_skl,X0)
| ~ relation(sK6_skl) ),
inference(resolution,[status(thm)],[f514,f499]) ).
fof(f524,definition,
! [X0] :
( sQ36_spl
<=> ( ~ in(ordered_pair(sK0_skl(X0,sK6_skl,sK6_skl),sK1_skl(X0,sK6_skl,sK6_skl)),sK6_skl)
| ~ in(sK0_skl(X0,sK6_skl,sK6_skl),X0)
| sK6_skl = relation_dom_restriction(sK6_skl,X0)
| sK6_skl = relation_dom_restriction(sK6_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f527,plain,
( sQ36_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f515,f304,f524]) ).
fof(f532,definition,
! [X0] :
( sQ37_spl
<=> sK6_skl = relation_dom_restriction(sK6_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f533,plain,
! [X0] :
( ~ sQ37_spl
| sK6_skl = relation_dom_restriction(sK6_skl,X0) ),
inference(component_clause,[status(thm)],[f532]) ).
fof(f535,plain,
( sQ37_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f520,f304,f532]) ).
fof(f548,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK10_skl,X1),X0),sK2_skl(sK0_skl(X2,relation_dom_restriction(sK10_skl,X1),X0),relation_dom(relation_dom_restriction(sK10_skl,X1)),relation_dom_restriction(sK10_skl,X1))),sK10_skl)
| ~ relation(sK10_skl)
| in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK10_skl,X1),X0),sK1_skl(X2,relation_dom_restriction(sK10_skl,X1),X0)),X0)
| relation_dom_restriction(sK10_skl,X1) = relation_dom_restriction(X0,X2)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f245,f167]) ).
fof(f552,definition,
! [X0,X1,X2] :
( sQ38_spl
<=> ( in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK10_skl,X1),X0),sK2_skl(sK0_skl(X2,relation_dom_restriction(sK10_skl,X1),X0),relation_dom(relation_dom_restriction(sK10_skl,X1)),relation_dom_restriction(sK10_skl,X1))),sK10_skl)
| in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK10_skl,X1),X0),sK1_skl(X2,relation_dom_restriction(sK10_skl,X1),X0)),X0)
| relation_dom_restriction(sK10_skl,X1) = relation_dom_restriction(X0,X2)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f555,plain,
( ~ sQ4_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f548,f552,f139]) ).
fof(f558,plain,
! [X0,X1] :
( ~ sQ37_spl
| ~ in(X0,relation_dom(sK6_skl))
| in(X0,X1)
| ~ relation(sK6_skl) ),
inference(paramodulation,[status(thm)],[f533,f197]) ).
fof(f559,plain,
! [X0,X1] :
( ~ sQ37_spl
| ~ in(X0,relation_dom(sK6_skl))
| in(ordered_pair(X0,sK2_skl(X0,relation_dom(relation_dom_restriction(sK6_skl,X1)),relation_dom_restriction(sK6_skl,X1))),sK6_skl)
| ~ relation(sK6_skl) ),
inference(paramodulation,[status(thm)],[f533,f167]) ).
fof(f560,plain,
! [X0,X1] :
( ~ sQ37_spl
| ~ in(X0,relation_dom(sK6_skl))
| ~ in(X0,X1)
| in(ordered_pair(X0,sK2_skl(X0,relation_dom(sK6_skl),sK6_skl)),sK6_skl)
| ~ relation(sK6_skl) ),
inference(paramodulation,[status(thm)],[f533,f165]) ).
fof(f561,plain,
! [X0,X1,X2] :
( ~ sQ37_spl
| in(X0,X2)
| ~ in(ordered_pair(X0,X1),sK6_skl)
| ~ relation(sK6_skl) ),
inference(paramodulation,[status(thm)],[f533,f151]) ).
fof(f562,plain,
! [X0,X1] :
( ~ sQ37_spl
| in(ordered_pair(X0,X1),sK6_skl)
| ~ in(ordered_pair(X0,X1),sK6_skl)
| ~ relation(sK6_skl) ),
inference(paramodulation,[status(thm)],[f533,f150]) ).
fof(f564,definition,
! [X0,X1] :
( sQ39_spl
<=> ( ~ in(X0,relation_dom(sK6_skl))
| in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f567,plain,
( ~ sQ37_spl
| sQ39_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f558,f304,f564,f532]) ).
fof(f568,definition,
! [X0,X1] :
( sQ40_spl
<=> ( ~ in(X0,relation_dom(sK6_skl))
| in(ordered_pair(X0,sK2_skl(X0,relation_dom(relation_dom_restriction(sK6_skl,X1)),relation_dom_restriction(sK6_skl,X1))),sK6_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f571,plain,
( ~ sQ37_spl
| sQ40_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f559,f304,f568,f532]) ).
fof(f572,definition,
! [X0,X1] :
( sQ41_spl
<=> ( ~ in(X0,relation_dom(sK6_skl))
| ~ in(X0,X1)
| in(ordered_pair(X0,sK2_skl(X0,relation_dom(sK6_skl),sK6_skl)),sK6_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f575,plain,
( ~ sQ37_spl
| sQ41_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f560,f304,f572,f532]) ).
fof(f576,definition,
! [X0,X1,X2] :
( sQ42_spl
<=> ( in(X0,X2)
| ~ in(ordered_pair(X0,X1),sK6_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f579,plain,
( ~ sQ37_spl
| sQ42_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f561,f304,f576,f532]) ).
fof(f580,definition,
! [X0,X1] :
( sQ43_spl
<=> ( in(ordered_pair(X0,X1),sK6_skl)
| ~ in(ordered_pair(X0,X1),sK6_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f583,plain,
( ~ sQ37_spl
| sQ43_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f562,f304,f580,f532]) ).
fof(f603,plain,
! [X0,X1,X2] :
( in(sK0_skl(X2,relation_dom_restriction(sK8_skl,X1),X0),X1)
| ~ relation(sK8_skl)
| in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK8_skl,X1),X0),sK1_skl(X2,relation_dom_restriction(sK8_skl,X1),X0)),X0)
| relation_dom_restriction(sK8_skl,X1) = relation_dom_restriction(X0,X2)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f193,f151]) ).
fof(f604,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK8_skl,X1),X0),sK1_skl(X2,relation_dom_restriction(sK8_skl,X1),X0)),sK8_skl)
| ~ relation(sK8_skl)
| in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK8_skl,X1),X0),sK1_skl(X2,relation_dom_restriction(sK8_skl,X1),X0)),X0)
| relation_dom_restriction(sK8_skl,X1) = relation_dom_restriction(X0,X2)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f193,f150]) ).
fof(f608,definition,
! [X0,X1,X2] :
( sQ44_spl
<=> ( in(sK0_skl(X2,relation_dom_restriction(sK8_skl,X1),X0),X1)
| in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK8_skl,X1),X0),sK1_skl(X2,relation_dom_restriction(sK8_skl,X1),X0)),X0)
| relation_dom_restriction(sK8_skl,X1) = relation_dom_restriction(X0,X2)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f611,plain,
( ~ sQ22_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f603,f608,f325]) ).
fof(f612,definition,
! [X0,X1,X2] :
( sQ45_spl
<=> ( in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK8_skl,X1),X0),sK1_skl(X2,relation_dom_restriction(sK8_skl,X1),X0)),sK8_skl)
| in(ordered_pair(sK0_skl(X2,relation_dom_restriction(sK8_skl,X1),X0),sK1_skl(X2,relation_dom_restriction(sK8_skl,X1),X0)),X0)
| relation_dom_restriction(sK8_skl,X1) = relation_dom_restriction(X0,X2)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f615,plain,
( ~ sQ22_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f604,f612,f325]) ).
fof(f623,plain,
( sQ15_spl
| ~ relation(relation_dom(sK6_skl)) ),
inference(forward_demodulation,[status(thm)],[f292,f284]) ).
fof(f624,plain,
( sQ15_spl
| ~ relation(sK6_skl) ),
inference(forward_demodulation,[status(thm)],[f450,f623]) ).
fof(f625,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f624,f75]) ).
fof(f626,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f625]) ).
fof(f638,plain,
! [X0] :
( in(ordered_pair(sK3_skl(empty_set,X0),sK4_skl(empty_set,X0)),X0)
| sK6_skl = relation_dom(X0)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f292,f210]) ).
fof(f639,plain,
! [X0] :
( in(ordered_pair(sK3_skl(sK6_skl,X0),sK4_skl(empty_set,X0)),X0)
| sK6_skl = relation_dom(X0)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f292,f638]) ).
fof(f640,plain,
! [X0] :
( in(ordered_pair(sK3_skl(sK6_skl,X0),sK4_skl(sK6_skl,X0)),X0)
| sK6_skl = relation_dom(X0)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f292,f639]) ).
fof(f646,plain,
( sK6_skl = relation_dom(sK6_skl)
| ~ relation(sK6_skl) ),
inference(resolution,[status(thm)],[f640,f499]) ).
fof(f655,definition,
( sQ46_spl
<=> sK6_skl = relation_dom(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f658,plain,
( sQ46_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f646,f304,f655]) ).
fof(f716,plain,
! [X0,X1] :
( in(ordered_pair(sK0_skl(empty_set,X1,X0),sK1_skl(empty_set,X1,X0)),X1)
| X1 = relation_dom_restriction(X0,sK6_skl)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f292,f212]) ).
fof(f717,plain,
! [X0,X1] :
( in(ordered_pair(sK0_skl(sK6_skl,X1,X0),sK1_skl(empty_set,X1,X0)),X1)
| X1 = relation_dom_restriction(X0,sK6_skl)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f292,f716]) ).
fof(f718,plain,
! [X0,X1] :
( in(ordered_pair(sK0_skl(sK6_skl,X1,X0),sK1_skl(sK6_skl,X1,X0)),X1)
| X1 = relation_dom_restriction(X0,sK6_skl)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f292,f717]) ).
fof(f724,plain,
! [X0] :
( sK6_skl = relation_dom_restriction(X0,sK6_skl)
| ~ relation(sK6_skl)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f718,f499]) ).
fof(f733,definition,
! [X0] :
( sQ48_spl
<=> ( sK6_skl = relation_dom_restriction(X0,sK6_skl)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f736,plain,
( ~ sQ18_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f724,f733,f304]) ).
fof(f743,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| in(ordered_pair(X0,sK2_skl(X0,sK6_skl,sK6_skl)),relation_dom_restriction(relation_dom_restriction(sK6_skl,X1),X2))
| ~ in(X0,relation_dom(sK6_skl))
| ~ in(X0,X1)
| ~ relation(sK6_skl) ),
inference(paramodulation,[status(thm)],[f450,f258]) ).
fof(f744,plain,
! [X0,X1,X2] :
( ~ sQ37_spl
| ~ in(X0,X2)
| in(ordered_pair(X0,sK2_skl(X0,relation_dom(sK6_skl),sK6_skl)),relation_dom_restriction(sK6_skl,X2))
| ~ in(X0,relation_dom(sK6_skl))
| ~ in(X0,X1)
| ~ relation(sK6_skl) ),
inference(paramodulation,[status(thm)],[f533,f258]) ).
fof(f745,definition,
! [X0,X1,X2] :
( sQ49_spl
<=> ( ~ in(X0,X2)
| in(ordered_pair(X0,sK2_skl(X0,sK6_skl,sK6_skl)),relation_dom_restriction(relation_dom_restriction(sK6_skl,X1),X2))
| ~ in(X0,relation_dom(sK6_skl))
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f748,plain,
( sQ49_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f743,f304,f745]) ).
fof(f749,definition,
! [X0,X1,X2] :
( sQ50_spl
<=> ( ~ in(X0,X2)
| in(ordered_pair(X0,sK2_skl(X0,relation_dom(sK6_skl),sK6_skl)),relation_dom_restriction(sK6_skl,X2))
| ~ in(X0,relation_dom(sK6_skl))
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f752,plain,
( ~ sQ37_spl
| sQ50_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f744,f304,f749,f532]) ).
fof(f770,plain,
! [X0,X1] :
( in(X0,relation_dom(relation_dom_restriction(sK10_skl,X1)))
| ~ in(X0,relation_dom(sK10_skl))
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f259,f96]) ).
fof(f773,plain,
! [X0,X1] :
( ~ sQ37_spl
| ~ in(sK6_skl,ordered_pair(X0,sK2_skl(X0,relation_dom(sK6_skl),sK6_skl)))
| ~ in(X0,relation_dom(sK6_skl))
| ~ in(X0,X1)
| ~ relation(sK6_skl) ),
inference(paramodulation,[status(thm)],[f533,f256]) ).
fof(f774,plain,
! [X0,X1] :
( ~ in(relation_dom_restriction(sK6_skl,X1),ordered_pair(X0,sK2_skl(X0,sK6_skl,sK6_skl)))
| ~ in(X0,relation_dom(sK6_skl))
| ~ in(X0,X1)
| ~ relation(sK6_skl) ),
inference(paramodulation,[status(thm)],[f450,f256]) ).
fof(f775,definition,
! [X0,X1] :
( sQ51_spl
<=> ( ~ in(sK6_skl,ordered_pair(X0,sK2_skl(X0,relation_dom(sK6_skl),sK6_skl)))
| ~ in(X0,relation_dom(sK6_skl))
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f778,plain,
( ~ sQ37_spl
| sQ51_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f773,f304,f775,f532]) ).
fof(f779,definition,
! [X0,X1] :
( sQ52_spl
<=> ( ~ in(relation_dom_restriction(sK6_skl,X1),ordered_pair(X0,sK2_skl(X0,sK6_skl,sK6_skl)))
| ~ in(X0,relation_dom(sK6_skl))
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f782,plain,
( sQ52_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f774,f304,f779]) ).
fof(f792,plain,
! [X0,X1] :
( relation_dom(relation_dom_restriction(X0,X1)) = relation_dom(sK6_skl)
| ~ relation(sK6_skl)
| in(ordered_pair(sK3_skl(relation_dom(relation_dom_restriction(X0,X1)),sK6_skl),sK2_skl(sK3_skl(relation_dom(relation_dom_restriction(X0,X1)),sK6_skl),relation_dom(relation_dom_restriction(X0,X1)),relation_dom_restriction(X0,X1))),X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f260,f499]) ).
fof(f796,plain,
! [X0,X1] :
( ~ sQ37_spl
| in(ordered_pair(sK3_skl(relation_dom(sK6_skl),X1),sK4_skl(relation_dom(relation_dom_restriction(sK6_skl,X0)),X1)),X1)
| relation_dom(relation_dom_restriction(sK6_skl,X0)) = relation_dom(X1)
| ~ relation(X1)
| in(ordered_pair(sK3_skl(relation_dom(relation_dom_restriction(sK6_skl,X0)),X1),sK2_skl(sK3_skl(relation_dom(relation_dom_restriction(sK6_skl,X0)),X1),relation_dom(relation_dom_restriction(sK6_skl,X0)),relation_dom_restriction(sK6_skl,X0))),sK6_skl)
| ~ relation(sK6_skl) ),
inference(paramodulation,[status(thm)],[f533,f260]) ).
fof(f797,plain,
! [X0,X1] :
( ~ sQ37_spl
| in(ordered_pair(sK3_skl(relation_dom(relation_dom_restriction(sK6_skl,X0)),X1),sK4_skl(relation_dom(sK6_skl),X1)),X1)
| relation_dom(relation_dom_restriction(sK6_skl,X0)) = relation_dom(X1)
| ~ relation(X1)
| in(ordered_pair(sK3_skl(relation_dom(relation_dom_restriction(sK6_skl,X0)),X1),sK2_skl(sK3_skl(relation_dom(relation_dom_restriction(sK6_skl,X0)),X1),relation_dom(relation_dom_restriction(sK6_skl,X0)),relation_dom_restriction(sK6_skl,X0))),sK6_skl)
| ~ relation(sK6_skl) ),
inference(paramodulation,[status(thm)],[f533,f260]) ).
fof(f803,definition,
! [X0,X1] :
( sQ53_spl
<=> ( relation_dom(relation_dom_restriction(X0,X1)) = relation_dom(sK6_skl)
| in(ordered_pair(sK3_skl(relation_dom(relation_dom_restriction(X0,X1)),sK6_skl),sK2_skl(sK3_skl(relation_dom(relation_dom_restriction(X0,X1)),sK6_skl),relation_dom(relation_dom_restriction(X0,X1)),relation_dom_restriction(X0,X1))),X0)
| ~ relation(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f806,plain,
( ~ sQ18_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f792,f803,f304]) ).
fof(f807,definition,
! [X0,X1] :
( sQ54_spl
<=> ( in(ordered_pair(sK3_skl(relation_dom(sK6_skl),X1),sK4_skl(relation_dom(relation_dom_restriction(sK6_skl,X0)),X1)),X1)
| relation_dom(relation_dom_restriction(sK6_skl,X0)) = relation_dom(X1)
| ~ relation(X1)
| in(ordered_pair(sK3_skl(relation_dom(relation_dom_restriction(sK6_skl,X0)),X1),sK2_skl(sK3_skl(relation_dom(relation_dom_restriction(sK6_skl,X0)),X1),relation_dom(relation_dom_restriction(sK6_skl,X0)),relation_dom_restriction(sK6_skl,X0))),sK6_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f810,plain,
( ~ sQ37_spl
| sQ54_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f796,f304,f807,f532]) ).
fof(f811,definition,
! [X0,X1] :
( sQ55_spl
<=> ( in(ordered_pair(sK3_skl(relation_dom(relation_dom_restriction(sK6_skl,X0)),X1),sK4_skl(relation_dom(sK6_skl),X1)),X1)
| relation_dom(relation_dom_restriction(sK6_skl,X0)) = relation_dom(X1)
| ~ relation(X1)
| in(ordered_pair(sK3_skl(relation_dom(relation_dom_restriction(sK6_skl,X0)),X1),sK2_skl(sK3_skl(relation_dom(relation_dom_restriction(sK6_skl,X0)),X1),relation_dom(relation_dom_restriction(sK6_skl,X0)),relation_dom_restriction(sK6_skl,X0))),sK6_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f814,plain,
( ~ sQ37_spl
| sQ55_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f797,f304,f811,f532]) ).
fof(f840,plain,
( sQ0_spl
| ~ in(sK11_skl,relation_dom(sK10_skl))
| ~ in(sK11_skl,sK12_skl) ),
inference(resolution,[status(thm)],[f770,f105]) ).
fof(f848,plain,
! [X0,X1] :
( in(X0,X1)
| ~ relation(sK10_skl)
| ~ in(X0,relation_dom(sK10_skl))
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f770,f197]) ).
fof(f849,plain,
! [X0,X1] :
( in(ordered_pair(X0,sK2_skl(X0,relation_dom(relation_dom_restriction(sK10_skl,X1)),relation_dom_restriction(sK10_skl,X1))),sK10_skl)
| ~ relation(sK10_skl)
| ~ in(X0,relation_dom(sK10_skl))
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f770,f167]) ).
fof(f851,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f840,f106,f110,f103]) ).
fof(f853,definition,
! [X0,X1] :
( sQ56_spl
<=> ( in(X0,X1)
| ~ in(X0,relation_dom(sK10_skl))
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f856,plain,
( ~ sQ4_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f848,f853,f139]) ).
fof(f857,definition,
! [X0,X1] :
( sQ57_spl
<=> ( in(ordered_pair(X0,sK2_skl(X0,relation_dom(relation_dom_restriction(sK10_skl,X1)),relation_dom_restriction(sK10_skl,X1))),sK10_skl)
| ~ in(X0,relation_dom(sK10_skl))
| ~ in(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f860,plain,
( ~ sQ4_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f849,f857,f139]) ).
fof(f861,plain,
( ~ sQ0_spl
| in(sK11_skl,sK12_skl)
| ~ relation(sK10_skl) ),
inference(resolution,[status(thm)],[f104,f197]) ).
fof(f864,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f861,f139,f106,f103]) ).
fof(f866,plain,
$false,
inference(sat_refutation,[status(thm)],[f109,f113,f114,f142,f146,f148,f164,f190,f219,f239,f243,f268,f270,f281,f288,f307,f311,f315,f317,f328,f332,f336,f338,f357,f358,f425,f432,f436,f438,f461,f468,f472,f478,f481,f506,f527,f535,f555,f567,f571,f575,f579,f583,f611,f615,f626,f658,f736,f748,f752,f778,f782,f806,f810,f814,f851,f856,f860,f864]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU192+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.39 % Computer : n015.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Mon Sep 21 05:59:56 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.15/5.41 % Drodi V4.1.1
% 0.15/5.55 % Refutation found
% 0.15/5.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/5.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.59 % Elapsed time: 0.178273 seconds
% 0.15/5.59 % CPU time: 1.107029 seconds
% 0.15/5.59 % Total memory used: 119.632 MB
% 0.15/5.59 % Net memory used: 117.763 MB
%------------------------------------------------------------------------------