%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET644+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 : n002.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 02:10:20 PM UTC 2026
% Result : Theorem 5.56s 1.39s
% Output : CNFRefutation 5.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 89 ( 13 unt; 0 def)
% Number of atoms : 362 ( 19 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 465 ( 192 ~; 184 |; 45 &)
% ( 10 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 192 ( 179 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( member(B,C)
=> ? [D] :
( ? [E] :
( B = ordered_pair(D,E)
& ilf_type(E,set_type) )
& ilf_type(D,set_type) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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)
=> ( member(ordered_pair(B,C),cross_product(D,E))
<=> ( member(C,E)
& member(B,D) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,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(f12,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(f14,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(f19,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(f20,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(f21,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(f24,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(f27,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,C))
=> ( member(D,E)
=> ? [F] :
( ? [G] :
( member(G,C)
& member(F,B)
& D = ordered_pair(F,G)
& ilf_type(G,set_type) )
& ilf_type(F,set_type) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,C))
=> ( member(D,E)
=> ? [F] :
( ? [G] :
( member(G,C)
& member(F,B)
& D = ordered_pair(F,G)
& ilf_type(G,set_type) )
& ilf_type(F,set_type) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f30,plain,
! [B] :
( ! [C] :
( ? [D] :
( ? [E] :
( B = ordered_pair(D,E)
& ilf_type(E,set_type) )
& ilf_type(D,set_type) )
| ~ member(B,C)
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f31,plain,
! [B] :
( ! [C] :
( ( B = ordered_pair(sK0_skl(C,B),sK1_skl(C,B))
& ilf_type(sK1_skl(C,B),set_type)
& ilf_type(sK0_skl(C,B),set_type) )
| ~ member(B,C)
| ~ ilf_type(C,binary_relation_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(D,sK0_skl(C,B)),skolemize(E,sK1_skl(C,B))],[f30]) ).
fof(f34,plain,
! [X0,X1] :
( X0 = ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0))
| ~ member(X0,X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f35,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( ( member(ordered_pair(B,C),cross_product(D,E))
<=> ( member(C,E)
& member(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)],[f2]) ).
fof(f36,plain,
! [B] :
( ! [C] :
( ! [D] :
( ! [E] :
( ( ( ~ member(C,E)
| ~ member(B,D)
| member(ordered_pair(B,C),cross_product(D,E)) )
& ( ( member(C,E)
& member(B,D) )
| ~ member(ordered_pair(B,C),cross_product(D,E)) ) )
| ~ ilf_type(E,set_type) )
| ~ ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(NNF_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ 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)],[f36]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ 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)],[f36]) ).
fof(f47,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)],[f5]) ).
fof(f49,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)],[f47]) ).
fof(f66,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)],[f12]) ).
fof(f67,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)],[f66]) ).
fof(f70,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)],[f67]) ).
fof(f73,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)],[f14]) ).
fof(f74,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)],[f73]) ).
fof(f75,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)],[f74]) ).
fof(f97,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)],[f19]) ).
fof(f98,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)],[f97]) ).
fof(f99,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK7_skl(C,B),C)
& member(sK7_skl(C,B),B)
& ilf_type(sK7_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,[sK7_skl]),skolemize(D,sK7_skl(C,B))],[f98]) ).
fof(f100,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)],[f99]) ).
fof(f104,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f105,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f107,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)],[f21]) ).
fof(f108,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)],[f107]) ).
fof(f109,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)],[f108]) ).
fof(f123,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)],[f24]) ).
fof(f124,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)],[f123]) ).
fof(f133,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f134,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ! [F] :
( ! [G] :
( ~ member(G,C)
| ~ member(F,B)
| D != ordered_pair(F,G)
| ~ ilf_type(G,set_type) )
| ~ ilf_type(F,set_type) )
& member(D,E)
& ilf_type(E,relation_type(B,C)) )
& ilf_type(D,set_type) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f135,plain,
( ! [F] :
( ! [G] :
( ~ member(G,sK14_skl)
| ~ member(F,sK13_skl)
| sK15_skl != ordered_pair(F,G)
| ~ ilf_type(G,set_type) )
| ~ ilf_type(F,set_type) )
& member(sK15_skl,sK16_skl)
& ilf_type(sK16_skl,relation_type(sK13_skl,sK14_skl))
& ilf_type(sK15_skl,set_type)
& ilf_type(sK14_skl,set_type)
& ilf_type(sK13_skl,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl,sK15_skl,sK16_skl]),skolemize(B,sK13_skl),skolemize(C,sK14_skl),skolemize(D,sK15_skl),skolemize(E,sK16_skl)],[f134]) ).
fof(f139,plain,
ilf_type(sK16_skl,relation_type(sK13_skl,sK14_skl)),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f140,plain,
member(sK15_skl,sK16_skl),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f141,plain,
! [X0,X1] :
( ~ member(X1,sK14_skl)
| ~ member(X0,sK13_skl)
| sK15_skl != ordered_pair(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f148,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(duplicate_literals_removal,[status(thm)],[f70]) ).
fof(f149,plain,
! [X0,X1] :
( ~ member(X1,sK14_skl)
| ~ member(X0,sK13_skl)
| sK15_skl != ordered_pair(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(backward_subsumption_resolution,[status(thm)],[f141,f133]) ).
fof(f150,plain,
! [X0,X1] :
( ~ member(X1,sK14_skl)
| ~ member(X0,sK13_skl)
| sK15_skl != ordered_pair(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f149,f133]) ).
fof(f152,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)],[f49,f133]) ).
fof(f154,plain,
! [X0] : ~ empty(power_set(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f105,f133]) ).
fof(f157,plain,
! [X0] :
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f148,f133]) ).
fof(f165,plain,
! [X0,X1] :
( X1 = ordered_pair(sK0_skl(X0,X1),sK1_skl(X0,X1))
| ~ member(X1,X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f34,f133]) ).
fof(f167,plain,
! [X0,X1] :
( ~ relation_like(X1)
| X0 = ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0))
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f165,f157]) ).
fof(f168,plain,
! [X0,X1,X2,X3] :
( member(X3,X1)
| ~ member(ordered_pair(X3,X0),cross_product(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f37,f133]) ).
fof(f169,plain,
! [X0,X1,X2,X3] :
( member(X0,X2)
| ~ member(ordered_pair(X3,X0),cross_product(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f38,f133]) ).
fof(f177,plain,
( ~ relation_like(sK16_skl)
| sK15_skl = ordered_pair(sK0_skl(sK16_skl,sK15_skl),sK1_skl(sK16_skl,sK15_skl)) ),
inference(resolution,[status(thm)],[f167,f140]) ).
fof(f224,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)],[f124,f133]) ).
fof(f225,plain,
! [X0,X1,X2] :
( relation_like(X0)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[f224,f133]) ).
fof(f227,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X2,X1))
| ~ ilf_type(X1,set_type)
| relation_like(X0) ),
inference(resolution,[status(thm)],[f225,f152]) ).
fof(f228,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f227,f133]) ).
fof(f231,plain,
! [X0,X1] :
( sK15_skl = ordered_pair(sK0_skl(sK16_skl,sK15_skl),sK1_skl(sK16_skl,sK15_skl))
| ~ ilf_type(sK16_skl,relation_type(X0,X1)) ),
inference(resolution,[status(thm)],[f228,f177]) ).
fof(f250,plain,
sK15_skl = ordered_pair(sK0_skl(sK16_skl,sK15_skl),sK1_skl(sK16_skl,sK15_skl)),
inference(resolution,[status(thm)],[f231,f139]) ).
fof(f258,plain,
! [X0,X1] :
( member(sK1_skl(sK16_skl,sK15_skl),X1)
| ~ member(sK15_skl,cross_product(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK1_skl(sK16_skl,sK15_skl),set_type) ),
inference(paramodulation,[status(thm)],[f250,f169]) ).
fof(f259,plain,
! [X0,X1] :
( member(sK0_skl(sK16_skl,sK15_skl),X0)
| ~ member(sK15_skl,cross_product(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK1_skl(sK16_skl,sK15_skl),set_type) ),
inference(paramodulation,[status(thm)],[f250,f168]) ).
fof(f262,plain,
! [X0,X1] :
( member(sK1_skl(sK16_skl,sK15_skl),X1)
| ~ member(sK15_skl,cross_product(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f258,f133]) ).
fof(f263,plain,
! [X0,X1] :
( member(sK0_skl(sK16_skl,sK15_skl),X0)
| ~ member(sK15_skl,cross_product(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f259,f133]) ).
fof(f380,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)],[f75,f133]) ).
fof(f439,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)],[f109,f133]) ).
fof(f440,plain,
! [X0,X1] :
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[f439,f133]) ).
fof(f442,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)],[f440,f380]) ).
fof(f444,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)],[f442,f154]) ).
fof(f465,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f444,f133]) ).
fof(f467,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| member(X0,power_set(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[f465,f152]) ).
fof(f469,plain,
! [X0,X1,X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
| member(X0,power_set(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f467,f133]) ).
fof(f476,plain,
member(sK16_skl,power_set(cross_product(sK13_skl,sK14_skl))),
inference(resolution,[status(thm)],[f469,f139]) ).
fof(f500,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)],[f100,f133]) ).
fof(f501,plain,
! [X0,X1,X2] :
( member(X2,X0)
| ~ member(X2,X1)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f500,f133]) ).
fof(f502,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f501,f133]) ).
fof(f526,plain,
! [X0] :
( member(X0,cross_product(sK13_skl,sK14_skl))
| ~ member(X0,sK16_skl) ),
inference(resolution,[status(thm)],[f502,f476]) ).
fof(f552,plain,
member(sK15_skl,cross_product(sK13_skl,sK14_skl)),
inference(resolution,[status(thm)],[f526,f140]) ).
fof(f2124,plain,
! [X0,X1] :
( member(sK1_skl(sK16_skl,sK15_skl),X0)
| ~ member(sK15_skl,cross_product(X1,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f262,f133]) ).
fof(f2125,plain,
( member(sK1_skl(sK16_skl,sK15_skl),sK14_skl)
| ~ ilf_type(sK14_skl,set_type) ),
inference(resolution,[status(thm)],[f2124,f552]) ).
fof(f2126,plain,
member(sK1_skl(sK16_skl,sK15_skl),sK14_skl),
inference(forward_subsumption_resolution,[status(thm)],[f2125,f133]) ).
fof(f2137,plain,
! [X0] :
( ~ member(X0,sK13_skl)
| sK15_skl != ordered_pair(X0,sK1_skl(sK16_skl,sK15_skl)) ),
inference(resolution,[status(thm)],[f2126,f150]) ).
fof(f3067,plain,
! [X0,X1] :
( member(sK0_skl(sK16_skl,sK15_skl),X1)
| ~ member(sK15_skl,cross_product(X1,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f263,f133]) ).
fof(f3068,plain,
( member(sK0_skl(sK16_skl,sK15_skl),sK13_skl)
| ~ ilf_type(sK14_skl,set_type) ),
inference(resolution,[status(thm)],[f3067,f552]) ).
fof(f3069,plain,
member(sK0_skl(sK16_skl,sK15_skl),sK13_skl),
inference(forward_subsumption_resolution,[status(thm)],[f3068,f133]) ).
fof(f3096,plain,
sK15_skl != ordered_pair(sK0_skl(sK16_skl,sK15_skl),sK1_skl(sK16_skl,sK15_skl)),
inference(resolution,[status(thm)],[f3069,f2137]) ).
fof(f3105,plain,
sK15_skl != sK15_skl,
inference(forward_demodulation,[status(thm)],[f250,f3096]) ).
fof(f3106,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f3105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET644+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n002.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Mon Sep 21 05:33:48 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.58 % Drodi V4.1.1
% 5.56/1.39 % Refutation found
% 5.56/1.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.56/1.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.88/1.44 % Elapsed time: 0.855229 seconds
% 2.88/1.44 % CPU time: 6.460194 seconds
% 2.88/1.44 % Total memory used: 200.657 MB
% 2.88/1.44 % Net memory used: 188.285 MB
%------------------------------------------------------------------------------