%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU195+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 : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:19:37 PM UTC 2026
% Result : Theorem 3.86s 0.91s
% Output : CNFRefutation 3.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 23
% Syntax : Number of formulae : 117 ( 12 unt; 13 def)
% Number of atoms : 408 ( 35 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 507 ( 216 ~; 219 |; 38 &)
% ( 23 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 14 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 195 ( 182 !; 13 ?)
% 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] :
( relation(B)
=> ( A = B
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
<=> in(ordered_pair(C,D),B) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(relation_composition(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] : relation(identity_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [A,B,C,D] :
( relation(D)
=> ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))
<=> ( in(ordered_pair(A,B),D)
& in(A,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,conjecture,
! [A,B] :
( relation(B)
=> relation_dom_restriction(B,A) = relation_composition(identity_relation(A),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> relation_dom_restriction(B,A) = relation_composition(identity_relation(A),B) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f36,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f40,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(f41,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)],[f40]) ).
fof(f42,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)],[f41]) ).
fof(f43,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))],[f42]) ).
fof(f44,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)],[f43]) ).
fof(f46,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)],[f43]) ).
fof(f47,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)],[f43]) ).
fof(f48,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)],[f43]) ).
fof(f49,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)],[f43]) ).
fof(f50,plain,
! [A] :
( ! [B] :
( ( A = B
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
<=> in(ordered_pair(C,D),B) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f51,plain,
! [A] :
( ! [B] :
( ( ( ? [C,D] :
( ( in(ordered_pair(C,D),B)
| in(ordered_pair(C,D),A) )
& ( ~ in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| A = B )
& ( ! [C,D] :
( ( ~ in(ordered_pair(C,D),B)
| in(ordered_pair(C,D),A) )
& ( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| A != B ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [A] :
( ! [B] :
( ( ( ? [C,D] :
( ( in(ordered_pair(C,D),B)
| in(ordered_pair(C,D),A) )
& ( ~ in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| A = B )
& ( ( ! [C,D] :
( ~ in(ordered_pair(C,D),B)
| in(ordered_pair(C,D),A) )
& ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| A != B ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f51]) ).
fof(f53,plain,
! [A] :
( ! [B] :
( ( ( ( ( in(ordered_pair(sK2_skl(B,A),sK3_skl(B,A)),B)
| in(ordered_pair(sK2_skl(B,A),sK3_skl(B,A)),A) )
& ( ~ in(ordered_pair(sK2_skl(B,A),sK3_skl(B,A)),B)
| ~ in(ordered_pair(sK2_skl(B,A),sK3_skl(B,A)),A) ) )
| A = B )
& ( ( ! [C,D] :
( ~ in(ordered_pair(C,D),B)
| in(ordered_pair(C,D),A) )
& ! [C,D] :
( in(ordered_pair(C,D),B)
| ~ in(ordered_pair(C,D),A) ) )
| A != B ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(C,sK2_skl(B,A)),skolemize(D,sK3_skl(B,A))],[f52]) ).
fof(f57,plain,
! [X0,X1] :
( in(ordered_pair(sK2_skl(X1,X0),sK3_skl(X1,X0)),X1)
| in(ordered_pair(sK2_skl(X1,X0),sK3_skl(X1,X0)),X0)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f59,plain,
! [A,B] :
( relation(relation_composition(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f60,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f62,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f63,plain,
! [A] :
( ! [B] : relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f62]) ).
fof(f64,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f84,plain,
( relation(sK7_skl)
& ~ empty(sK7_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl]),skolemize(A,sK7_skl)],[f25]) ).
fof(f85,plain,
~ empty(sK7_skl),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f86,plain,
relation(sK7_skl),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f91,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f92,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f95,plain,
! [A,B,C,D] :
( ( in(ordered_pair(A,B),relation_composition(identity_relation(C),D))
<=> ( in(ordered_pair(A,B),D)
& in(A,C) ) )
| ~ relation(D) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f96,plain,
! [A,B,C,D] :
( ( ( ~ in(ordered_pair(A,B),D)
| ~ in(A,C)
| in(ordered_pair(A,B),relation_composition(identity_relation(C),D)) )
& ( ( in(ordered_pair(A,B),D)
& in(A,C) )
| ~ in(ordered_pair(A,B),relation_composition(identity_relation(C),D)) ) )
| ~ relation(D) ),
inference(NNF_transformation,[status(thm)],[f95]) ).
fof(f97,plain,
! [D] :
( ( ! [A,B,C] :
( ~ in(ordered_pair(A,B),D)
| ~ in(A,C)
| in(ordered_pair(A,B),relation_composition(identity_relation(C),D)) )
& ! [A,B,C] :
( ( in(ordered_pair(A,B),D)
& in(A,C) )
| ~ in(ordered_pair(A,B),relation_composition(identity_relation(C),D)) ) )
| ~ relation(D) ),
inference(miniscoping,[status(thm)],[f96]) ).
fof(f98,plain,
! [X0,X1,X2,X3] :
( in(X1,X3)
| ~ in(ordered_pair(X1,X2),relation_composition(identity_relation(X3),X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f99,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X1,X2),relation_composition(identity_relation(X3),X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f100,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X1,X2),X0)
| ~ in(X1,X3)
| in(ordered_pair(X1,X2),relation_composition(identity_relation(X3),X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f107,plain,
? [A,B] :
( relation_dom_restriction(B,A) != relation_composition(identity_relation(A),B)
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f108,plain,
? [B] :
( ? [A] : relation_dom_restriction(B,A) != relation_composition(identity_relation(A),B)
& relation(B) ),
inference(miniscoping,[status(thm)],[f107]) ).
fof(f109,plain,
( relation_dom_restriction(sK9_skl,sK10_skl) != relation_composition(identity_relation(sK10_skl),sK9_skl)
& relation(sK9_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl]),skolemize(B,sK9_skl),skolemize(A,sK10_skl)],[f108]) ).
fof(f110,plain,
relation(sK9_skl),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f111,plain,
relation_dom_restriction(sK9_skl,sK10_skl) != relation_composition(identity_relation(sK10_skl),sK9_skl),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f112,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)],[f44]) ).
fof(f114,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)],[f46]) ).
fof(f115,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)],[f114,f64]) ).
fof(f117,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)],[f112,f64]) ).
fof(f138,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f117,f36]) ).
fof(f183,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X1,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f115,f138]) ).
fof(f187,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| ~ in(X1,X1)
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f183]) ).
fof(f237,plain,
! [X0,X1] :
( in(ordered_pair(sK2_skl(X1,X0),sK3_skl(X1,X0)),X1)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0)
| ~ in(sK2_skl(X1,X0),sK2_skl(X1,X0))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f187,f57]) ).
fof(f249,plain,
! [X0,X1,X2] :
( empty(X0)
| ~ element(ordered_pair(X1,X2),X0)
| ~ in(X1,X1)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f187,f92]) ).
fof(f253,plain,
! [X0,X1] :
( in(ordered_pair(sK2_skl(X1,X0),sK3_skl(X1,X0)),X1)
| X0 = X1
| ~ relation(X1)
| ~ in(sK2_skl(X1,X0),sK2_skl(X1,X0))
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f237]) ).
fof(f254,plain,
! [X0,X1] :
( X0 = X1
| ~ relation(X1)
| ~ in(sK2_skl(X1,X0),sK2_skl(X1,X0))
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f187]) ).
fof(f296,plain,
( ~ relation(relation_composition(identity_relation(sK10_skl),sK9_skl))
| ~ in(sK2_skl(relation_composition(identity_relation(sK10_skl),sK9_skl),relation_dom_restriction(sK9_skl,sK10_skl)),sK2_skl(relation_composition(identity_relation(sK10_skl),sK9_skl),relation_dom_restriction(sK9_skl,sK10_skl)))
| ~ relation(relation_dom_restriction(sK9_skl,sK10_skl)) ),
inference(resolution,[status(thm)],[f254,f111]) ).
fof(f297,plain,
( ~ relation(relation_dom_restriction(sK9_skl,sK10_skl))
| ~ in(sK2_skl(relation_dom_restriction(sK9_skl,sK10_skl),relation_composition(identity_relation(sK10_skl),sK9_skl)),sK2_skl(relation_dom_restriction(sK9_skl,sK10_skl),relation_composition(identity_relation(sK10_skl),sK9_skl)))
| ~ relation(relation_composition(identity_relation(sK10_skl),sK9_skl)) ),
inference(resolution,[status(thm)],[f254,f111]) ).
fof(f298,definition,
( sQ0_spl
<=> relation(relation_dom_restriction(sK9_skl,sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f300,plain,
( sQ0_spl
| ~ relation(relation_dom_restriction(sK9_skl,sK10_skl)) ),
inference(component_clause,[status(thm)],[f298]) ).
fof(f301,definition,
( sQ1_spl
<=> in(sK2_skl(relation_composition(identity_relation(sK10_skl),sK9_skl),relation_dom_restriction(sK9_skl,sK10_skl)),sK2_skl(relation_composition(identity_relation(sK10_skl),sK9_skl),relation_dom_restriction(sK9_skl,sK10_skl))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f304,definition,
( sQ2_spl
<=> relation(relation_composition(identity_relation(sK10_skl),sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f306,plain,
( sQ2_spl
| ~ relation(relation_composition(identity_relation(sK10_skl),sK9_skl)) ),
inference(component_clause,[status(thm)],[f304]) ).
fof(f307,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f296,f298,f301,f304]) ).
fof(f308,definition,
( sQ3_spl
<=> in(sK2_skl(relation_dom_restriction(sK9_skl,sK10_skl),relation_composition(identity_relation(sK10_skl),sK9_skl)),sK2_skl(relation_dom_restriction(sK9_skl,sK10_skl),relation_composition(identity_relation(sK10_skl),sK9_skl))) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f311,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f297,f304,f308,f298]) ).
fof(f312,plain,
( sQ0_spl
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f300,f64]) ).
fof(f314,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f312,f110]) ).
fof(f315,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f314]) ).
fof(f318,plain,
( sQ2_spl
| ~ relation(sK9_skl)
| ~ relation(identity_relation(sK10_skl)) ),
inference(resolution,[status(thm)],[f306,f60]) ).
fof(f323,definition,
( sQ5_spl
<=> relation(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f325,plain,
( sQ5_spl
| ~ relation(sK9_skl) ),
inference(component_clause,[status(thm)],[f323]) ).
fof(f330,definition,
( sQ7_spl
<=> relation(identity_relation(sK10_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f332,plain,
( sQ7_spl
| ~ relation(identity_relation(sK10_skl)) ),
inference(component_clause,[status(thm)],[f330]) ).
fof(f334,plain,
( sQ2_spl
| ~ sQ5_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f318,f330,f323,f304]) ).
fof(f335,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f325,f110]) ).
fof(f336,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f335]) ).
fof(f337,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f332,f61]) ).
fof(f338,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f337]) ).
fof(f507,plain,
! [X0,X1] :
( ~ element(ordered_pair(X0,X1),sK7_skl)
| ~ in(X0,X0)
| ~ relation(sK7_skl) ),
inference(resolution,[status(thm)],[f85,f249]) ).
fof(f508,definition,
( sQ14_spl
<=> relation(sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f510,plain,
( sQ14_spl
| ~ relation(sK7_skl) ),
inference(component_clause,[status(thm)],[f508]) ).
fof(f511,definition,
! [X0,X1] :
( sQ15_spl
<=> ( ~ element(ordered_pair(X0,X1),sK7_skl)
| ~ in(X0,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f514,plain,
( sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f507,f508,f511]) ).
fof(f515,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f510,f86]) ).
fof(f516,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f515]) ).
fof(f517,plain,
( ~ in(ordered_pair(sK0_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl),sK1_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl)),sK9_skl)
| ~ in(sK0_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl),sK10_skl)
| ~ in(ordered_pair(sK0_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl),sK1_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl)),relation_composition(identity_relation(sK10_skl),sK9_skl))
| ~ relation(relation_composition(identity_relation(sK10_skl),sK9_skl))
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f47,f111]) ).
fof(f518,definition,
( sQ16_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl),sK1_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl)),relation_composition(identity_relation(sK10_skl),sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f519,plain,
( ~ sQ16_spl
| in(ordered_pair(sK0_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl),sK1_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl)),relation_composition(identity_relation(sK10_skl),sK9_skl)) ),
inference(component_clause,[status(thm)],[f518]) ).
fof(f520,plain,
( sQ16_spl
| ~ in(ordered_pair(sK0_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl),sK1_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl)),relation_composition(identity_relation(sK10_skl),sK9_skl)) ),
inference(component_clause,[status(thm)],[f518]) ).
fof(f521,definition,
( sQ17_spl
<=> in(sK0_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl),sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f523,plain,
( sQ17_spl
| ~ in(sK0_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl),sK10_skl) ),
inference(component_clause,[status(thm)],[f521]) ).
fof(f524,definition,
( sQ18_spl
<=> in(ordered_pair(sK0_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl),sK1_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl)),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f526,plain,
( sQ18_spl
| ~ in(ordered_pair(sK0_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl),sK1_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl)),sK9_skl) ),
inference(component_clause,[status(thm)],[f524]) ).
fof(f527,plain,
( ~ sQ18_spl
| ~ sQ17_spl
| ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f517,f323,f304,f518,f521,f524]) ).
fof(f613,plain,
! [X0] :
( sQ18_spl
| ~ in(ordered_pair(sK0_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl),sK1_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl)),relation_composition(identity_relation(X0),sK9_skl))
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f526,f99]) ).
fof(f620,definition,
( sQ24_spl
<=> relation_composition(identity_relation(sK10_skl),sK9_skl) = relation_dom_restriction(sK9_skl,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f621,plain,
( ~ sQ24_spl
| relation_composition(identity_relation(sK10_skl),sK9_skl) = relation_dom_restriction(sK9_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f620]) ).
fof(f636,definition,
! [X0] :
( sQ28_spl
<=> ~ in(ordered_pair(sK0_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl),sK1_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl)),relation_composition(identity_relation(X0),sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f637,plain,
! [X0] :
( ~ sQ28_spl
| ~ in(ordered_pair(sK0_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl),sK1_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl)),relation_composition(identity_relation(X0),sK9_skl)) ),
inference(component_clause,[status(thm)],[f636]) ).
fof(f639,plain,
( sQ18_spl
| sQ28_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f613,f323,f636,f524]) ).
fof(f674,plain,
( ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f621,f111]) ).
fof(f675,plain,
~ sQ24_spl,
inference(contradiction_clause,[status(thm)],[f674]) ).
fof(f740,plain,
( sQ16_spl
| in(ordered_pair(sK0_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl),sK1_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl)),sK9_skl)
| relation_composition(identity_relation(sK10_skl),sK9_skl) = relation_dom_restriction(sK9_skl,sK10_skl)
| ~ relation(relation_composition(identity_relation(sK10_skl),sK9_skl))
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f520,f49]) ).
fof(f742,plain,
( sQ16_spl
| ~ in(ordered_pair(sK0_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl),sK1_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl)),sK9_skl)
| ~ in(sK0_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl),sK10_skl)
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f520,f100]) ).
fof(f748,plain,
( sQ16_spl
| sQ18_spl
| sQ24_spl
| ~ sQ2_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f740,f323,f304,f620,f524,f518]) ).
fof(f750,plain,
( sQ16_spl
| ~ sQ18_spl
| ~ sQ17_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f742,f323,f521,f524,f518]) ).
fof(f805,plain,
! [X0,X1] :
( sQ17_spl
| ~ in(ordered_pair(sK0_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl),X1),relation_composition(identity_relation(sK10_skl),X0))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f523,f98]) ).
fof(f894,plain,
( sQ17_spl
| in(sK0_skl(sK10_skl,relation_composition(identity_relation(sK10_skl),sK9_skl),sK9_skl),sK10_skl)
| relation_composition(identity_relation(sK10_skl),sK9_skl) = relation_dom_restriction(sK9_skl,sK10_skl)
| ~ relation(relation_composition(identity_relation(sK10_skl),sK9_skl))
| ~ relation(sK9_skl)
| ~ relation(sK9_skl) ),
inference(resolution,[status(thm)],[f805,f48]) ).
fof(f903,plain,
( sQ17_spl
| sQ24_spl
| ~ sQ2_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f894,f323,f304,f620,f521]) ).
fof(f905,plain,
( ~ sQ16_spl
| ~ sQ28_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f519,f637]) ).
fof(f906,plain,
( ~ sQ16_spl
| ~ sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f905]) ).
fof(f907,plain,
$false,
inference(sat_refutation,[status(thm)],[f307,f311,f315,f334,f336,f338,f514,f516,f527,f639,f675,f748,f750,f903,f906]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU195+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:56:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 3.86/0.91 % Refutation found
% 3.86/0.91 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.86/0.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.86/0.94 % Elapsed time: 0.567141 seconds
% 3.86/0.94 % CPU time: 4.132690 seconds
% 3.86/0.94 % Total memory used: 168.665 MB
% 3.86/0.94 % Net memory used: 160.573 MB
%------------------------------------------------------------------------------