%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET655+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 : n016.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 02:10:22 PM UTC 2026
% Result : Theorem 2.78s 0.90s
% Output : CNFRefutation 3.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 95 ( 14 unt; 0 def)
% Number of atoms : 380 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 492 ( 207 ~; 199 |; 40 &)
% ( 10 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 212 ( 204 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ( ( subset(D,E)
& subset(B,C) )
=> subset(cross_product(B,D),cross_product(C,E)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,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(f5,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,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(f10,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(f11,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(f12,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(f14,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(f19,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ! [F] :
( ilf_type(F,relation_type(B,D))
=> ( ( subset(D,E)
& subset(B,C) )
=> ilf_type(F,relation_type(C,E)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ! [F] :
( ilf_type(F,relation_type(B,D))
=> ( ( subset(D,E)
& subset(B,C) )
=> ilf_type(F,relation_type(C,E)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f24,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( subset(cross_product(B,D),cross_product(C,E))
| ~ subset(D,E)
| ~ subset(B,C)
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,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)],[f3]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,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)],[f26]) ).
fof(f32,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)],[f5]) ).
fof(f33,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)],[f32]) ).
fof(f34,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK1_skl(C,B),C)
& member(sK1_skl(C,B),B)
& ilf_type(sK1_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,[sK1_skl]),skolemize(D,sK1_skl(C,B))],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f41,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)],[f7]) ).
fof(f42,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)],[f41]) ).
fof(f43,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)],[f42]) ).
fof(f44,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)],[f42]) ).
fof(f50,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)],[f10]) ).
fof(f51,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)],[f50]) ).
fof(f52,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK3_skl(C,B),C)
& member(sK3_skl(C,B),B)
& ilf_type(sK3_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,[sK3_skl]),skolemize(D,sK3_skl(C,B))],[f51]) ).
fof(f53,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)],[f52]) ).
fof(f55,plain,
! [X0,X1] :
( member(sK3_skl(X1,X0),X0)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f56,plain,
! [X0,X1] :
( ~ member(sK3_skl(X1,X0),X1)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f57,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f58,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f60,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)],[f12]) ).
fof(f61,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)],[f60]) ).
fof(f62,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)],[f61]) ).
fof(f63,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)],[f61]) ).
fof(f67,plain,
! [B] :
( ( empty(B)
<=> ! [C] :
( ~ member(C,B)
| ~ ilf_type(C,set_type) ) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f68,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)],[f67]) ).
fof(f69,plain,
! [B] :
( ( ( ( member(sK5_skl(B),B)
& ilf_type(sK5_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,[sK5_skl]),skolemize(C,sK5_skl(B))],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f88,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f89,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ? [F] :
( ~ ilf_type(F,relation_type(C,E))
& subset(D,E)
& subset(B,C)
& ilf_type(F,relation_type(B,D)) )
& ilf_type(E,set_type) )
& ilf_type(D,set_type) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f90,plain,
( ~ ilf_type(sK13_skl,relation_type(sK10_skl,sK12_skl))
& subset(sK11_skl,sK12_skl)
& subset(sK9_skl,sK10_skl)
& ilf_type(sK13_skl,relation_type(sK9_skl,sK11_skl))
& ilf_type(sK12_skl,set_type)
& ilf_type(sK11_skl,set_type)
& ilf_type(sK10_skl,set_type)
& ilf_type(sK9_skl,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl,sK11_skl,sK12_skl,sK13_skl]),skolemize(B,sK9_skl),skolemize(C,sK10_skl),skolemize(D,sK11_skl),skolemize(E,sK12_skl),skolemize(F,sK13_skl)],[f89]) ).
fof(f95,plain,
ilf_type(sK13_skl,relation_type(sK9_skl,sK11_skl)),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f96,plain,
subset(sK9_skl,sK10_skl),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f97,plain,
subset(sK11_skl,sK12_skl),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f98,plain,
~ ilf_type(sK13_skl,relation_type(sK10_skl,sK12_skl)),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f99,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)],[f63,f70]) ).
fof(f108,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)],[f62,f88]) ).
fof(f109,plain,
! [X0] : ~ empty(power_set(X0)),
inference(backward_subsumption_resolution,[status(thm)],[f58,f88]) ).
fof(f110,plain,
! [X0,X1] :
( ~ member(sK3_skl(X1,X0),X1)
| member(X0,power_set(X1))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f56,f88]) ).
fof(f111,plain,
! [X0,X1] :
( member(sK3_skl(X1,X0),X0)
| member(X0,power_set(X1))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f55,f88]) ).
fof(f112,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)],[f53,f88]) ).
fof(f115,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)],[f44,f88]) ).
fof(f116,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)],[f43,f88]) ).
fof(f119,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f35,f88]) ).
fof(f121,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)],[f28,f88]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ilf_type(X1,relation_type(X0,X2))
| ~ ilf_type(X1,subset_type(cross_product(X0,X2)))
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f27,f88]) ).
fof(f123,plain,
! [X0,X1,X2,X3] :
( subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f25,f88]) ).
fof(f125,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f99,f88]) ).
fof(f130,plain,
! [X0,X1] :
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f88]) ).
fof(f131,plain,
! [X0,X1] :
( ~ member(sK3_skl(X1,X0),X1)
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f110,f88]) ).
fof(f132,plain,
! [X0,X1] :
( member(sK3_skl(X1,X0),X0)
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f111,f88]) ).
fof(f133,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)],[f112,f88]) ).
fof(f134,plain,
! [X0,X1] :
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f115,f88]) ).
fof(f135,plain,
! [X0,X1] :
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f116,f88]) ).
fof(f138,plain,
! [X0,X1,X2] :
( member(X2,X0)
| ~ member(X2,X1)
| ~ subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f119,f88]) ).
fof(f140,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)],[f121,f88]) ).
fof(f141,plain,
! [X0,X1,X2] :
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f122,f88]) ).
fof(f142,plain,
! [X0,X1,X2,X3] :
( subset(cross_product(X2,X1),cross_product(X0,X3))
| ~ subset(X1,X3)
| ~ subset(X2,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f123,f88]) ).
fof(f144,plain,
~ ilf_type(sK13_skl,subset_type(cross_product(sK10_skl,sK12_skl))),
inference(resolution,[status(thm)],[f141,f98]) ).
fof(f148,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(resolution,[status(thm)],[f130,f109]) ).
fof(f151,plain,
! [X0,X1,X2] :
( member(sK3_skl(X1,X0),X2)
| ~ subset(X0,X2)
| ~ ilf_type(X2,set_type)
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f132,f138]) ).
fof(f153,plain,
! [X0,X1,X2] :
( member(sK3_skl(X1,X0),X2)
| ~ subset(X0,X2)
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f88]) ).
fof(f161,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f133,f88]) ).
fof(f164,plain,
~ ilf_type(sK13_skl,member_type(power_set(cross_product(sK10_skl,sK12_skl)))),
inference(resolution,[status(thm)],[f134,f144]) ).
fof(f165,plain,
( ~ member(sK13_skl,power_set(cross_product(sK10_skl,sK12_skl)))
| ~ ilf_type(power_set(cross_product(sK10_skl,sK12_skl)),set_type) ),
inference(resolution,[status(thm)],[f164,f125]) ).
fof(f166,plain,
~ member(sK13_skl,power_set(cross_product(sK10_skl,sK12_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f165,f88]) ).
fof(f169,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f148,f135]) ).
fof(f175,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| member(X0,power_set(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[f169,f140]) ).
fof(f188,plain,
! [X0,X1,X2] :
( member(X2,power_set(X1))
| ~ member(sK3_skl(X1,X2),X0)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f161,f131]) ).
fof(f205,plain,
member(sK13_skl,power_set(cross_product(sK9_skl,sK11_skl))),
inference(resolution,[status(thm)],[f175,f95]) ).
fof(f218,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ subset(X0,X1)
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f153,f131]) ).
fof(f220,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| member(X0,power_set(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f218]) ).
fof(f241,plain,
! [X0,X1,X2,X3] :
( ~ subset(X1,X3)
| ~ subset(X0,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(cross_product(X0,X1),power_set(cross_product(X2,X3))) ),
inference(resolution,[status(thm)],[f220,f142]) ).
fof(f247,plain,
! [X0,X1,X2,X3] :
( ~ subset(X1,X3)
| ~ subset(X0,X2)
| ~ ilf_type(X1,set_type)
| member(cross_product(X0,X1),power_set(cross_product(X2,X3))) ),
inference(forward_subsumption_resolution,[status(thm)],[f241,f88]) ).
fof(f272,plain,
! [X0,X1,X2,X3] :
( ~ member(sK3_skl(X1,X2),X3)
| ~ member(X3,power_set(X0))
| member(X2,power_set(X1))
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f188,f161]) ).
fof(f567,plain,
! [X0,X1,X2] :
( member(X2,power_set(X1))
| ~ member(X2,power_set(X0))
| member(X2,power_set(X1))
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f272,f132]) ).
fof(f576,plain,
! [X0,X1,X2] :
( ~ member(X2,power_set(X0))
| member(X2,power_set(X1))
| ~ member(X0,power_set(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f567]) ).
fof(f616,plain,
! [X0] :
( ~ member(sK13_skl,power_set(X0))
| ~ member(X0,power_set(cross_product(sK10_skl,sK12_skl))) ),
inference(resolution,[status(thm)],[f576,f166]) ).
fof(f632,plain,
~ member(cross_product(sK9_skl,sK11_skl),power_set(cross_product(sK10_skl,sK12_skl))),
inference(resolution,[status(thm)],[f616,f205]) ).
fof(f640,plain,
( ~ subset(sK11_skl,sK12_skl)
| ~ subset(sK9_skl,sK10_skl)
| ~ ilf_type(sK11_skl,set_type) ),
inference(resolution,[status(thm)],[f632,f247]) ).
fof(f643,plain,
( ~ subset(sK11_skl,sK12_skl)
| ~ subset(sK9_skl,sK10_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f640,f88]) ).
fof(f644,plain,
~ subset(sK9_skl,sK10_skl),
inference(resolution,[status(thm)],[f643,f97]) ).
fof(f647,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f644,f96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET655+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 05:36:07 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 2.78/0.90 % Refutation found
% 2.78/0.90 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.78/0.90 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.22/0.94 % Elapsed time: 0.550095 seconds
% 3.22/0.94 % CPU time: 3.829110 seconds
% 3.22/0.94 % Total memory used: 134.709 MB
% 3.22/0.94 % Net memory used: 127.949 MB
%------------------------------------------------------------------------------