%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET678+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 02:10:25 PM UTC 2026
% Result : Theorem 0.13s 0.46s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 30
% Syntax : Number of formulae : 160 ( 13 unt; 12 def)
% Number of atoms : 515 ( 36 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 605 ( 250 ~; 255 |; 30 &)
% ( 24 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 13 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 4 con; 0-3 aty)
% Number of variables : 234 ( 230 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(domain_of(C),B)
=> compose(identity_relation_of(B),C) = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(range_of(C),B)
=> compose(C,identity_relation_of(B)) = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [B] :
( ilf_type(B,set_type)
=> ilf_type(identity_relation_of(B),binary_relation_type) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,identity_relation_of_type(B))
<=> ilf_type(C,relation_type(B,B)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) )
& ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> relation_like(D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> domain(B,C,D) = domain_of(D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(domain(B,C,D),subset_type(B)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> range(B,C,D) = range_of(D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(range(B,C,D),subset_type(C)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,identity_relation_of_type(B))
=> ( compose(identity_relation_of(B),C) = C
& compose(C,identity_relation_of(B)) = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,identity_relation_of_type(B))
=> ( compose(identity_relation_of(B),C) = C
& compose(C,identity_relation_of(B)) = C ) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f41,plain,
! [B] :
( ! [C] :
( compose(identity_relation_of(B),C) = C
| ~ subset(domain_of(C),B)
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f42,plain,
! [X0,X1] :
( compose(identity_relation_of(X0),X1) = X1
| ~ subset(domain_of(X1),X0)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [B] :
( ! [C] :
( compose(C,identity_relation_of(B)) = C
| ~ subset(range_of(C),B)
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f44,plain,
! [X0,X1] :
( compose(X1,identity_relation_of(X0)) = X1
| ~ subset(range_of(X1),X0)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f59,plain,
! [B] :
( ilf_type(identity_relation_of(B),binary_relation_type)
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f60,plain,
! [X0] :
( ilf_type(identity_relation_of(X0),binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [B] :
( ! [C] :
( ( ilf_type(C,identity_relation_of_type(B))
<=> ilf_type(C,relation_type(B,B)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f62,plain,
! [B] :
( ! [C] :
( ( ( ~ ilf_type(C,relation_type(B,B))
| ilf_type(C,identity_relation_of_type(B)) )
& ( ilf_type(C,relation_type(B,B))
| ~ ilf_type(C,identity_relation_of_type(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ilf_type(X1,relation_type(X0,X0))
| ~ ilf_type(X1,identity_relation_of_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f83,plain,
! [B] :
( ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f84,plain,
! [B] :
( ( ( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) )
& ( ( ilf_type(B,set_type)
& relation_like(B) )
| ~ ilf_type(B,binary_relation_type) ) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f83]) ).
fof(f87,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f90,plain,
! [B] :
( ! [C] :
( ( ! [E] :
( ilf_type(E,subset_type(cross_product(B,C)))
| ~ ilf_type(E,relation_type(B,C)) )
& ! [D] :
( ilf_type(D,relation_type(B,C))
| ~ ilf_type(D,subset_type(cross_product(B,C))) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f100,plain,
! [B] :
( ! [C] :
( ( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f101,plain,
! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ subset(B,C) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f100]) ).
fof(f102,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK6_skl(C,B),C)
& member(sK6_skl(C,B),B)
& ilf_type(sK6_skl(C,B),set_type) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ subset(B,C) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(D,sK6_skl(C,B))],[f101]) ).
fof(f105,plain,
! [X0,X1] :
( member(sK6_skl(X1,X0),X0)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f106,plain,
! [X0,X1] :
( ~ member(sK6_skl(X1,X0),X1)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f111,plain,
! [B] :
( ! [C] :
( ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f112,plain,
! [B] :
( ! [C] :
( ( ( ~ ilf_type(C,member_type(power_set(B)))
| ilf_type(C,subset_type(B)) )
& ( ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,subset_type(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f127,plain,
! [B] :
( ! [C] :
( ! [D] :
( relation_like(D)
| ~ ilf_type(D,subset_type(cross_product(B,C))) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f128,plain,
! [X0,X1,X2] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f129,plain,
! [B] :
( ! [C] :
( ( member(B,power_set(C))
<=> ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f130,plain,
! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) )
| member(B,power_set(C)) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f129]) ).
fof(f131,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK11_skl(C,B),C)
& member(sK11_skl(C,B),B)
& ilf_type(sK11_skl(C,B),set_type) )
| member(B,power_set(C)) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B)
| ~ ilf_type(D,set_type) )
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(D,sK11_skl(C,B))],[f130]) ).
fof(f132,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f136,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f137,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f139,plain,
! [B] :
( ! [C] :
( ( ilf_type(B,member_type(C))
<=> member(B,C) )
| ~ ilf_type(C,set_type)
| empty(C) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f140,plain,
! [B] :
( ! [C] :
( ( ( ~ member(B,C)
| ilf_type(B,member_type(C)) )
& ( member(B,C)
| ~ ilf_type(B,member_type(C)) ) )
| ~ ilf_type(C,set_type)
| empty(C) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f139]) ).
fof(f141,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f154,plain,
! [B] :
( ! [C] :
( ! [D] :
( domain(B,C,D) = domain_of(D)
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f155,plain,
! [X0,X1,X2] :
( domain(X0,X1,X2) = domain_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f156,plain,
! [B] :
( ! [C] :
( ! [D] :
( ilf_type(domain(B,C,D),subset_type(B))
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f157,plain,
! [X0,X1,X2] :
( ilf_type(domain(X0,X1,X2),subset_type(X0))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f158,plain,
! [B] :
( ! [C] :
( ! [D] :
( range(B,C,D) = range_of(D)
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f159,plain,
! [X0,X1,X2] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f158]) ).
fof(f160,plain,
! [B] :
( ! [C] :
( ! [D] :
( ilf_type(range(B,C,D),subset_type(C))
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f161,plain,
! [X0,X1,X2] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f166,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f167,plain,
? [B] :
( ? [C] :
( ( compose(identity_relation_of(B),C) != C
| compose(C,identity_relation_of(B)) != C )
& ilf_type(C,identity_relation_of_type(B)) )
& ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f168,plain,
( ( compose(identity_relation_of(sK14_skl),sK15_skl) != sK15_skl
| compose(sK15_skl,identity_relation_of(sK14_skl)) != sK15_skl )
& ilf_type(sK15_skl,identity_relation_of_type(sK14_skl))
& ilf_type(sK14_skl,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl]),skolemize(B,sK14_skl),skolemize(C,sK15_skl)],[f167]) ).
fof(f170,plain,
ilf_type(sK15_skl,identity_relation_of_type(sK14_skl)),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f171,plain,
( compose(identity_relation_of(sK14_skl),sK15_skl) != sK15_skl
| compose(sK15_skl,identity_relation_of(sK14_skl)) != sK15_skl ),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f172,definition,
( sQ0_spl
<=> compose(sK15_skl,identity_relation_of(sK14_skl)) = sK15_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f175,definition,
( sQ1_spl
<=> compose(identity_relation_of(sK14_skl),sK15_skl) = sK15_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f171,f172,f175]) ).
fof(f181,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literals_removal,[status(thm)],[f87]) ).
fof(f184,plain,
! [X0] : ilf_type(identity_relation_of(X0),binary_relation_type),
inference(forward_subsumption_resolution,[status(thm)],[f60,f166]) ).
fof(f186,plain,
! [X0,X1] :
( ilf_type(X0,relation_type(X1,X1))
| ~ ilf_type(X0,identity_relation_of_type(X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f63,f166]) ).
fof(f193,plain,
! [X0] : ~ empty(power_set(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f137,f166]) ).
fof(f199,plain,
! [X0,X1] :
( compose(identity_relation_of(X1),X0) = X0
| ~ subset(domain_of(X0),X1)
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f42,f166]) ).
fof(f201,plain,
! [X0,X1] :
( compose(X0,identity_relation_of(X1)) = X0
| ~ subset(range_of(X0),X1)
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f44,f166]) ).
fof(f260,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f181,f166]) ).
fof(f347,plain,
! [X0,X1] :
( member(sK6_skl(X0,X1),X1)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f105,f166]) ).
fof(f348,plain,
! [X0,X1] :
( ~ member(sK6_skl(X0,X1),X0)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f106,f166]) ).
fof(f349,plain,
! [X0,X1] :
( ~ member(sK6_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f348,f166]) ).
fof(f498,plain,
! [X0,X1,X2] :
( relation_like(X1)
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f128,f166]) ).
fof(f499,plain,
! [X0,X1,X2] :
( ilf_type(X1,binary_relation_type)
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f498,f260]) ).
fof(f500,plain,
! [X0,X1,X2] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f499,f166]) ).
fof(f529,plain,
! [X0,X1,X2] :
( ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f92,f166]) ).
fof(f530,plain,
! [X0,X1,X2] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f529,f166]) ).
fof(f534,plain,
! [X0,X1] :
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f113,f166]) ).
fof(f537,plain,
! [X0,X1,X2] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f530,f500]) ).
fof(f540,plain,
! [X0,X1] :
( ~ ilf_type(X0,identity_relation_of_type(X1))
| ~ ilf_type(X0,set_type)
| ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[f537,f186]) ).
fof(f542,plain,
! [X0,X1] :
( ~ ilf_type(X0,identity_relation_of_type(X1))
| ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f540,f166]) ).
fof(f567,plain,
ilf_type(sK15_skl,binary_relation_type),
inference(resolution,[status(thm)],[f542,f170]) ).
fof(f607,definition,
( sQ22_spl
<=> ilf_type(sK15_skl,binary_relation_type) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f609,plain,
( sQ22_spl
| ~ ilf_type(sK15_skl,binary_relation_type) ),
inference(component_clause,[status(thm)],[f607]) ).
fof(f628,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f609,f567]) ).
fof(f629,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f628]) ).
fof(f667,plain,
! [X0,X1] :
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f141,f166]) ).
fof(f668,plain,
! [X0,X1] :
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[f667,f166]) ).
fof(f670,plain,
! [X0,X1] :
( ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| member(X1,power_set(X0))
| empty(power_set(X0)) ),
inference(resolution,[status(thm)],[f668,f534]) ).
fof(f672,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type)
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f670,f193]) ).
fof(f742,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f672,f166]) ).
fof(f838,plain,
! [X0,X1,X2] :
( member(X2,X0)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f132,f166]) ).
fof(f839,plain,
! [X0,X1,X2] :
( member(X2,X0)
| ~ member(X2,X1)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f838,f166]) ).
fof(f840,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f839,f166]) ).
fof(f1056,plain,
! [X0,X1,X2] :
( domain(X2,X0,X1) = domain_of(X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f166]) ).
fof(f1057,plain,
! [X0,X1,X2] :
( domain(X1,X2,X0) = domain_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f1056,f166]) ).
fof(f1058,plain,
! [X0,X1,X2] :
( ilf_type(domain(X2,X0,X1),subset_type(X2))
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f157,f166]) ).
fof(f1059,plain,
! [X0,X1,X2] :
( ilf_type(domain(X1,X2,X0),subset_type(X1))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f1058,f166]) ).
fof(f1116,plain,
! [X0,X1] :
( ~ ilf_type(X1,identity_relation_of_type(X0))
| ~ ilf_type(X1,set_type)
| domain(X0,X0,X1) = domain_of(X1) ),
inference(resolution,[status(thm)],[f1057,f186]) ).
fof(f1119,plain,
! [X0,X1] :
( ~ ilf_type(X1,identity_relation_of_type(X0))
| domain(X0,X0,X1) = domain_of(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1116,f166]) ).
fof(f1124,plain,
domain(sK14_skl,sK14_skl,sK15_skl) = domain_of(sK15_skl),
inference(resolution,[status(thm)],[f1119,f170]) ).
fof(f1127,plain,
( ilf_type(domain_of(sK15_skl),subset_type(sK14_skl))
| ~ ilf_type(sK15_skl,relation_type(sK14_skl,sK14_skl)) ),
inference(paramodulation,[status(thm)],[f1124,f1059]) ).
fof(f1128,definition,
( sQ47_spl
<=> ilf_type(sK15_skl,relation_type(sK14_skl,sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f1129,plain,
( ~ sQ47_spl
| ilf_type(sK15_skl,relation_type(sK14_skl,sK14_skl)) ),
inference(component_clause,[status(thm)],[f1128]) ).
fof(f1130,plain,
( sQ47_spl
| ~ ilf_type(sK15_skl,relation_type(sK14_skl,sK14_skl)) ),
inference(component_clause,[status(thm)],[f1128]) ).
fof(f1131,definition,
( sQ48_spl
<=> ilf_type(domain_of(sK15_skl),subset_type(sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f1132,plain,
( ~ sQ48_spl
| ilf_type(domain_of(sK15_skl),subset_type(sK14_skl)) ),
inference(component_clause,[status(thm)],[f1131]) ).
fof(f1134,plain,
( sQ48_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f1127,f1128,f1131]) ).
fof(f1136,plain,
( sQ47_spl
| ~ ilf_type(sK15_skl,identity_relation_of_type(sK14_skl))
| ~ ilf_type(sK15_skl,set_type) ),
inference(resolution,[status(thm)],[f1130,f186]) ).
fof(f1137,definition,
( sQ49_spl
<=> ilf_type(sK14_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f1139,plain,
( sQ49_spl
| ~ ilf_type(sK14_skl,set_type) ),
inference(component_clause,[status(thm)],[f1137]) ).
fof(f1144,definition,
( sQ51_spl
<=> ilf_type(sK15_skl,set_type) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f1146,plain,
( sQ51_spl
| ~ ilf_type(sK15_skl,set_type) ),
inference(component_clause,[status(thm)],[f1144]) ).
fof(f1147,definition,
( sQ52_spl
<=> ilf_type(sK15_skl,identity_relation_of_type(sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f1149,plain,
( sQ52_spl
| ~ ilf_type(sK15_skl,identity_relation_of_type(sK14_skl)) ),
inference(component_clause,[status(thm)],[f1147]) ).
fof(f1150,plain,
( sQ47_spl
| ~ sQ52_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f1136,f1144,f1147,f1128]) ).
fof(f1151,plain,
( sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1139,f166]) ).
fof(f1152,plain,
sQ49_spl,
inference(contradiction_clause,[status(thm)],[f1151]) ).
fof(f1153,plain,
( sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1146,f166]) ).
fof(f1154,plain,
sQ51_spl,
inference(contradiction_clause,[status(thm)],[f1153]) ).
fof(f1155,plain,
( sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1149,f170]) ).
fof(f1156,plain,
sQ52_spl,
inference(contradiction_clause,[status(thm)],[f1155]) ).
fof(f1157,plain,
( ~ sQ48_spl
| member(domain_of(sK15_skl),power_set(sK14_skl)) ),
inference(resolution,[status(thm)],[f1132,f742]) ).
fof(f1161,plain,
! [X0] :
( ~ sQ48_spl
| member(X0,sK14_skl)
| ~ member(X0,domain_of(sK15_skl)) ),
inference(resolution,[status(thm)],[f1157,f840]) ).
fof(f1165,plain,
! [X0] :
( ~ sQ48_spl
| subset(X0,sK14_skl)
| ~ member(sK6_skl(sK14_skl,X0),domain_of(sK15_skl)) ),
inference(resolution,[status(thm)],[f1161,f349]) ).
fof(f1167,plain,
! [X0,X1,X2] :
( range(X2,X0,X1) = range_of(X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f159,f166]) ).
fof(f1168,plain,
! [X0,X1,X2] :
( range(X1,X2,X0) = range_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f1167,f166]) ).
fof(f1169,plain,
! [X0,X1,X2] :
( ilf_type(range(X2,X0,X1),subset_type(X0))
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f161,f166]) ).
fof(f1170,plain,
! [X0,X1,X2] :
( ilf_type(range(X1,X2,X0),subset_type(X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[f1169,f166]) ).
fof(f1174,plain,
( ~ sQ48_spl
| subset(domain_of(sK15_skl),sK14_skl)
| ~ ilf_type(sK14_skl,set_type)
| subset(domain_of(sK15_skl),sK14_skl) ),
inference(resolution,[status(thm)],[f1165,f347]) ).
fof(f1176,definition,
( sQ53_spl
<=> subset(domain_of(sK15_skl),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f1177,plain,
( ~ sQ53_spl
| subset(domain_of(sK15_skl),sK14_skl) ),
inference(component_clause,[status(thm)],[f1176]) ).
fof(f1179,plain,
( ~ sQ48_spl
| ~ sQ49_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f1174,f1176,f1137,f1131]) ).
fof(f1181,plain,
( ~ sQ53_spl
| compose(identity_relation_of(sK14_skl),sK15_skl) = sK15_skl
| ~ ilf_type(sK15_skl,binary_relation_type) ),
inference(resolution,[status(thm)],[f1177,f199]) ).
fof(f1183,plain,
( ~ sQ53_spl
| sQ1_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f1181,f607,f175,f1176]) ).
fof(f1190,definition,
( sQ55_spl
<=> ilf_type(identity_relation_of(sK14_skl),binary_relation_type) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f1192,plain,
( sQ55_spl
| ~ ilf_type(identity_relation_of(sK14_skl),binary_relation_type) ),
inference(component_clause,[status(thm)],[f1190]) ).
fof(f1199,plain,
( sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1192,f184]) ).
fof(f1200,plain,
sQ55_spl,
inference(contradiction_clause,[status(thm)],[f1199]) ).
fof(f1217,plain,
( ~ sQ47_spl
| range(sK14_skl,sK14_skl,sK15_skl) = range_of(sK15_skl) ),
inference(resolution,[status(thm)],[f1168,f1129]) ).
fof(f1228,plain,
( ~ sQ47_spl
| ilf_type(range_of(sK15_skl),subset_type(sK14_skl))
| ~ ilf_type(sK15_skl,relation_type(sK14_skl,sK14_skl)) ),
inference(paramodulation,[status(thm)],[f1217,f1170]) ).
fof(f1230,definition,
( sQ57_spl
<=> ilf_type(range_of(sK15_skl),subset_type(sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f1231,plain,
( ~ sQ57_spl
| ilf_type(range_of(sK15_skl),subset_type(sK14_skl)) ),
inference(component_clause,[status(thm)],[f1230]) ).
fof(f1233,plain,
( sQ57_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f1228,f1128,f1230]) ).
fof(f1241,plain,
( ~ sQ57_spl
| member(range_of(sK15_skl),power_set(sK14_skl)) ),
inference(resolution,[status(thm)],[f1231,f742]) ).
fof(f1242,plain,
! [X0] :
( ~ sQ57_spl
| member(X0,sK14_skl)
| ~ member(X0,range_of(sK15_skl)) ),
inference(resolution,[status(thm)],[f1241,f840]) ).
fof(f1247,plain,
! [X0] :
( ~ sQ57_spl
| subset(X0,sK14_skl)
| ~ member(sK6_skl(sK14_skl,X0),range_of(sK15_skl)) ),
inference(resolution,[status(thm)],[f1242,f349]) ).
fof(f1249,plain,
( ~ sQ57_spl
| subset(range_of(sK15_skl),sK14_skl)
| ~ ilf_type(sK14_skl,set_type)
| subset(range_of(sK15_skl),sK14_skl) ),
inference(resolution,[status(thm)],[f1247,f347]) ).
fof(f1251,definition,
( sQ58_spl
<=> subset(range_of(sK15_skl),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f1252,plain,
( ~ sQ58_spl
| subset(range_of(sK15_skl),sK14_skl) ),
inference(component_clause,[status(thm)],[f1251]) ).
fof(f1254,plain,
( ~ sQ57_spl
| ~ sQ49_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f1249,f1251,f1137,f1230]) ).
fof(f1256,plain,
( ~ sQ58_spl
| compose(sK15_skl,identity_relation_of(sK14_skl)) = sK15_skl
| ~ ilf_type(sK15_skl,binary_relation_type) ),
inference(resolution,[status(thm)],[f1252,f201]) ).
fof(f1258,plain,
( ~ sQ58_spl
| sQ0_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f1256,f607,f172,f1251]) ).
fof(f1259,plain,
$false,
inference(sat_refutation,[status(thm)],[f178,f629,f1134,f1150,f1152,f1154,f1156,f1179,f1183,f1200,f1233,f1254,f1258]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET678+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:32:25 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.46 % Refutation found
% 0.13/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.49 % Elapsed time: 0.117052 seconds
% 0.13/0.49 % CPU time: 0.667166 seconds
% 0.13/0.49 % Total memory used: 99.334 MB
% 0.13/0.49 % Net memory used: 98.179 MB
%------------------------------------------------------------------------------