%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET682+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 02:10:26 PM UTC 2026
% Result : Theorem 0.16s 0.50s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 97 ( 20 unt; 0 def)
% Number of atoms : 351 ( 12 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 428 ( 174 ~; 159 |; 44 &)
% ( 10 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 184 ( 174 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( member(B,domain_of(C))
=> ? [D] :
( member(D,range_of(C))
& ilf_type(D,set_type) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,conjecture,
! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ! [E] :
( ilf_type(E,member_type(B))
=> ( member(E,domain(B,C,D))
=> ? [F] :
( member(F,range(B,C,D))
& ilf_type(F,member_type(C)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
~ ! [B] :
( ( ilf_type(B,set_type)
& ~ empty(B) )
=> ! [C] :
( ( ilf_type(C,set_type)
& ~ empty(C) )
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ! [E] :
( ilf_type(E,member_type(B))
=> ( member(E,domain(B,C,D))
=> ? [F] :
( member(F,range(B,C,D))
& ilf_type(F,member_type(C)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f27,plain,
! [B] :
( ! [C] :
( ? [D] :
( member(D,range_of(C))
& ilf_type(D,set_type) )
| ~ member(B,domain_of(C))
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f28,plain,
! [B] :
( ! [C] :
( ( member(sK0_skl(C,B),range_of(C))
& ilf_type(sK0_skl(C,B),set_type) )
| ~ member(B,domain_of(C))
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f27]) ).
fof(f30,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),range_of(X1))
| ~ member(X0,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f31,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)],[f2]) ).
fof(f33,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)],[f31]) ).
fof(f37,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)],[f4]) ).
fof(f38,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)],[f37]) ).
fof(f39,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)],[f38]) ).
fof(f40,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)],[f38]) ).
fof(f44,plain,
! [B] :
( ( empty(B)
<=> ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) ) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f45,plain,
! [B] :
( ( ( ? [C] :
( member(C,B)
& ilf_type(C,set_type) )
| empty(B) )
& ( ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) )
| ~ empty(B) ) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [B] :
( ( ( ( member(sK3_skl(B),B)
& ilf_type(sK3_skl(B),set_type) )
| empty(B) )
& ( ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) )
| ~ empty(B) ) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(C,sK3_skl(B))],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f56,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)],[f10]) ).
fof(f57,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)],[f56]) ).
fof(f60,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)],[f57]) ).
fof(f63,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)],[f12]) ).
fof(f64,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)],[f63]) ).
fof(f65,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)],[f64]) ).
fof(f70,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)],[f14]) ).
fof(f71,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)],[f70]) ).
fof(f72,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK6_skl(C,B),C)
& member(sK6_skl(C,B),B)
& ilf_type(sK6_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,[sK6_skl]),skolemize(D,sK6_skl(C,B))],[f71]) ).
fof(f73,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)],[f72]) ).
fof(f77,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f78,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f91,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)],[f18]) ).
fof(f92,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)],[f91]) ).
fof(f95,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)],[f20]) ).
fof(f96,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)],[f95]) ).
fof(f99,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)],[f22]) ).
fof(f100,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)],[f99]) ).
fof(f101,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)],[f23]) ).
fof(f102,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)],[f101]) ).
fof(f103,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f104,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ! [F] :
( ~ member(F,range(B,C,D))
| ~ ilf_type(F,member_type(C)) )
& member(E,domain(B,C,D))
& ilf_type(E,member_type(B)) )
& ilf_type(D,relation_type(B,C)) )
& ilf_type(C,set_type)
& ~ empty(C) )
& ilf_type(B,set_type)
& ~ empty(B) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f105,plain,
( ! [F] :
( ~ member(F,range(sK10_skl,sK11_skl,sK12_skl))
| ~ ilf_type(F,member_type(sK11_skl)) )
& member(sK13_skl,domain(sK10_skl,sK11_skl,sK12_skl))
& ilf_type(sK13_skl,member_type(sK10_skl))
& ilf_type(sK12_skl,relation_type(sK10_skl,sK11_skl))
& ilf_type(sK11_skl,set_type)
& ~ empty(sK11_skl)
& ilf_type(sK10_skl,set_type)
& ~ empty(sK10_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl,sK13_skl]),skolemize(B,sK10_skl),skolemize(C,sK11_skl),skolemize(D,sK12_skl),skolemize(E,sK13_skl)],[f104]) ).
fof(f110,plain,
ilf_type(sK12_skl,relation_type(sK10_skl,sK11_skl)),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f112,plain,
member(sK13_skl,domain(sK10_skl,sK11_skl,sK12_skl)),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f113,plain,
! [X0] :
( ~ member(X0,range(sK10_skl,sK11_skl,sK12_skl))
| ~ ilf_type(X0,member_type(sK11_skl)) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f114,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f40,f47]) ).
fof(f115,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literals_removal,[status(thm)],[f60]) ).
fof(f116,plain,
! [X0,X1,X2] :
( ilf_type(range(X0,X2,X1),subset_type(X2))
| ~ ilf_type(X1,relation_type(X0,X2))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f102,f103]) ).
fof(f117,plain,
! [X0,X1,X2] :
( range(X0,X2,X1) = range_of(X1)
| ~ ilf_type(X1,relation_type(X0,X2))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f100,f103]) ).
fof(f119,plain,
! [X0,X1,X2] :
( domain(X0,X2,X1) = domain_of(X1)
| ~ ilf_type(X1,relation_type(X0,X2))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f96,f103]) ).
fof(f120,plain,
! [X0,X1,X2] :
( relation_like(X1)
| ~ ilf_type(X1,subset_type(cross_product(X0,X2)))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f92,f103]) ).
fof(f125,plain,
! [X0] : ~ empty(power_set(X0)),
inference(backward_subsumption_resolution,[status(thm)],[f78,f103]) ).
fof(f128,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f73,f103]) ).
fof(f131,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f65,f103]) ).
fof(f132,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f115,f103]) ).
fof(f137,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f39,f103]) ).
fof(f139,plain,
! [X0,X1,X2] :
( ilf_type(X1,subset_type(cross_product(X0,X2)))
| ~ ilf_type(X1,relation_type(X0,X2))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f33,f103]) ).
fof(f141,plain,
! [X0,X1] :
( member(sK0_skl(X0,X1),range_of(X0))
| ~ member(X1,domain_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f30,f103]) ).
fof(f142,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f114,f103]) ).
fof(f143,plain,
! [X0,X1,X2] :
( ilf_type(range(X1,X2,X0),subset_type(X2))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f116,f103]) ).
fof(f144,plain,
! [X0,X1,X2] :
( range(X1,X2,X0) = range_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f117,f103]) ).
fof(f146,plain,
! [X0,X1,X2] :
( domain(X1,X2,X0) = domain_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f119,f103]) ).
fof(f147,plain,
! [X0,X1,X2] :
( relation_like(X0)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f103]) ).
fof(f152,plain,
! [X0,X1,X2] :
( member(X2,X0)
| ~ member(X2,X1)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f128,f103]) ).
fof(f154,plain,
! [X0,X1] :
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f131,f103]) ).
fof(f156,plain,
! [X0,X1] :
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f137,f103]) ).
fof(f158,plain,
! [X0,X1,X2] :
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f139,f103]) ).
fof(f173,plain,
ilf_type(range(sK10_skl,sK11_skl,sK12_skl),subset_type(sK11_skl)),
inference(resolution,[status(thm)],[f143,f110]) ).
fof(f210,plain,
range(sK10_skl,sK11_skl,sK12_skl) = range_of(sK12_skl),
inference(resolution,[status(thm)],[f144,f110]) ).
fof(f213,plain,
! [X0] :
( ~ member(X0,range_of(sK12_skl))
| ~ ilf_type(X0,member_type(sK11_skl)) ),
inference(backward_demodulation,[status(thm)],[f210,f113]) ).
fof(f216,plain,
ilf_type(range_of(sK12_skl),subset_type(sK11_skl)),
inference(backward_demodulation,[status(thm)],[f210,f173]) ).
fof(f226,plain,
domain(sK10_skl,sK11_skl,sK12_skl) = domain_of(sK12_skl),
inference(resolution,[status(thm)],[f146,f110]) ).
fof(f229,plain,
member(sK13_skl,domain_of(sK12_skl)),
inference(backward_demodulation,[status(thm)],[f226,f112]) ).
fof(f263,plain,
ilf_type(range_of(sK12_skl),member_type(power_set(sK11_skl))),
inference(resolution,[status(thm)],[f154,f216]) ).
fof(f281,plain,
( member(range_of(sK12_skl),power_set(sK11_skl))
| empty(power_set(sK11_skl)) ),
inference(resolution,[status(thm)],[f263,f156]) ).
fof(f282,plain,
member(range_of(sK12_skl),power_set(sK11_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f281,f125]) ).
fof(f303,plain,
! [X0] :
( member(X0,sK11_skl)
| ~ member(X0,range_of(sK12_skl))
| ~ ilf_type(sK11_skl,set_type) ),
inference(resolution,[status(thm)],[f152,f282]) ).
fof(f313,plain,
! [X0] :
( member(X0,sK11_skl)
| ~ member(X0,range_of(sK12_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f303,f103]) ).
fof(f322,plain,
ilf_type(sK12_skl,subset_type(cross_product(sK10_skl,sK11_skl))),
inference(resolution,[status(thm)],[f158,f110]) ).
fof(f349,plain,
relation_like(sK12_skl),
inference(resolution,[status(thm)],[f322,f147]) ).
fof(f351,plain,
ilf_type(sK12_skl,binary_relation_type),
inference(resolution,[status(thm)],[f349,f132]) ).
fof(f389,plain,
( member(sK0_skl(sK12_skl,sK13_skl),range_of(sK12_skl))
| ~ ilf_type(sK12_skl,binary_relation_type) ),
inference(resolution,[status(thm)],[f141,f229]) ).
fof(f390,plain,
member(sK0_skl(sK12_skl,sK13_skl),range_of(sK12_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f389,f351]) ).
fof(f394,plain,
member(sK0_skl(sK12_skl,sK13_skl),sK11_skl),
inference(resolution,[status(thm)],[f390,f313]) ).
fof(f395,plain,
~ ilf_type(sK0_skl(sK12_skl,sK13_skl),member_type(sK11_skl)),
inference(resolution,[status(thm)],[f390,f213]) ).
fof(f405,plain,
( ilf_type(sK0_skl(sK12_skl,sK13_skl),member_type(sK11_skl))
| ~ ilf_type(sK11_skl,set_type) ),
inference(resolution,[status(thm)],[f394,f142]) ).
fof(f408,plain,
ilf_type(sK0_skl(sK12_skl,sK13_skl),member_type(sK11_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f405,f103]) ).
fof(f409,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f395,f408]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET682+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n006.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 05:32:12 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 0.16/0.50 % Refutation found
% 0.16/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.72/0.54 % Elapsed time: 0.104574 seconds
% 0.72/0.54 % CPU time: 0.464463 seconds
% 0.72/0.54 % Total memory used: 86.128 MB
% 0.72/0.54 % Net memory used: 85.692 MB
%------------------------------------------------------------------------------