%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET645+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 : n017.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 0.09s 0.61s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 71 ( 10 unt; 2 def)
% Number of atoms : 277 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 345 ( 139 ~; 136 |; 31 &)
% ( 10 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 163 ( 157 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,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(f10,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(f13,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(f14,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(f15,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(f21,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,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,C))
=> ( member(ordered_pair(D,E),F)
=> ( member(E,C)
& member(D,B) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,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,C))
=> ( member(ordered_pair(D,E),F)
=> ( member(E,C)
& member(D,B) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f24,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)],[f1]) ).
fof(f25,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)],[f24]) ).
fof(f26,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)],[f25]) ).
fof(f27,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)],[f25]) ).
fof(f36,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)],[f4]) ).
fof(f38,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)],[f36]) ).
fof(f50,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)],[f10]) ).
fof(f51,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)],[f50]) ).
fof(f52,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)],[f51]) ).
fof(f65,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)],[f13]) ).
fof(f66,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)],[f65]) ).
fof(f67,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))],[f66]) ).
fof(f68,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)],[f67]) ).
fof(f72,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f73,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f75,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)],[f15]) ).
fof(f76,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)],[f75]) ).
fof(f77,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)],[f76]) ).
fof(f101,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f102,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ? [F] :
( ( ~ member(E,C)
| ~ member(D,B) )
& member(ordered_pair(D,E),F)
& ilf_type(F,relation_type(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)],[f23]) ).
fof(f103,plain,
( ( ~ member(sK12_skl,sK10_skl)
| ~ member(sK11_skl,sK9_skl) )
& member(ordered_pair(sK11_skl,sK12_skl),sK13_skl)
& ilf_type(sK13_skl,relation_type(sK9_skl,sK10_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)],[f102]) ).
fof(f108,plain,
ilf_type(sK13_skl,relation_type(sK9_skl,sK10_skl)),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f109,plain,
member(ordered_pair(sK11_skl,sK12_skl),sK13_skl),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f110,plain,
( ~ member(sK12_skl,sK10_skl)
| ~ member(sK11_skl,sK9_skl) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f122,definition,
( sQ3_spl
<=> member(sK11_skl,sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f124,plain,
( sQ3_spl
| ~ member(sK11_skl,sK9_skl) ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f125,definition,
( sQ4_spl
<=> member(sK12_skl,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f127,plain,
( sQ4_spl
| ~ member(sK12_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f110,f122,f125]) ).
fof(f130,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)],[f38,f101]) ).
fof(f131,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)],[f26,f101]) ).
fof(f138,plain,
! [X0] : ~ empty(power_set(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f73,f101]) ).
fof(f143,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)],[f27,f101]) ).
fof(f176,plain,
! [X0,X1,X2,X3] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f143,f101]) ).
fof(f177,plain,
! [X0,X1,X2,X3] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f131,f101]) ).
fof(f178,plain,
! [X0,X1,X2,X3] :
( member(X2,X0)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f176,f101]) ).
fof(f201,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)],[f52,f101]) ).
fof(f213,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X0))
| ~ ilf_type(X0,set_type) ),
inference(forward_subsumption_resolution,[status(thm)],[f177,f101]) ).
fof(f476,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)],[f68,f101]) ).
fof(f477,plain,
! [X0,X1,X2] :
( member(X2,X0)
| ~ member(X2,X1)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[f476,f101]) ).
fof(f478,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f477,f101]) ).
fof(f480,plain,
! [X0,X1,X2,X3,X4] :
( member(X3,X1)
| ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X3,X4),X0)
| ~ member(X0,power_set(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[f478,f213]) ).
fof(f481,plain,
! [X0,X1,X2,X3,X4] :
( member(X4,X2)
| ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X3,X4),X0)
| ~ member(X0,power_set(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[f478,f178]) ).
fof(f484,plain,
! [X0,X1,X2,X3,X4] :
( member(X3,X1)
| ~ member(ordered_pair(X3,X4),X0)
| ~ member(X0,power_set(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f480,f101]) ).
fof(f485,plain,
! [X0,X1,X2,X3,X4] :
( member(X4,X2)
| ~ member(ordered_pair(X3,X4),X0)
| ~ member(X0,power_set(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[f481,f101]) ).
fof(f490,plain,
! [X0,X1] :
( member(sK11_skl,X0)
| ~ member(sK13_skl,power_set(cross_product(X0,X1))) ),
inference(resolution,[status(thm)],[f484,f109]) ).
fof(f498,plain,
! [X0,X1] :
( member(sK12_skl,X1)
| ~ member(sK13_skl,power_set(cross_product(X0,X1))) ),
inference(resolution,[status(thm)],[f485,f109]) ).
fof(f613,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)],[f77,f101]) ).
fof(f614,plain,
! [X0,X1] :
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[f613,f101]) ).
fof(f623,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(resolution,[status(thm)],[f614,f138]) ).
fof(f628,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type)
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[f623,f201]) ).
fof(f631,plain,
! [X0,X1] :
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f628,f101]) ).
fof(f633,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)],[f631,f130]) ).
fof(f635,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)],[f633,f101]) ).
fof(f643,plain,
member(sK13_skl,power_set(cross_product(sK9_skl,sK10_skl))),
inference(resolution,[status(thm)],[f635,f108]) ).
fof(f646,plain,
member(sK11_skl,sK9_skl),
inference(resolution,[status(thm)],[f643,f490]) ).
fof(f648,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f646,f124]) ).
fof(f649,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f648]) ).
fof(f650,plain,
! [X0] :
( sQ4_spl
| ~ member(sK13_skl,power_set(cross_product(X0,sK10_skl))) ),
inference(resolution,[status(thm)],[f127,f498]) ).
fof(f652,plain,
( sQ4_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f643,f650]) ).
fof(f654,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f652]) ).
fof(f655,plain,
$false,
inference(sat_refutation,[status(thm)],[f128,f649,f654]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET645+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n017.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Mon Sep 21 05:26:13 UTC 2026
% 0.09/0.56 % CPUTime :
% 0.09/0.57 % Drodi V4.1.1
% 0.09/0.61 % Refutation found
% 0.09/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.63 % Elapsed time: 0.061643 seconds
% 0.13/0.63 % CPU time: 0.266536 seconds
% 0.13/0.63 % Total memory used: 71.898 MB
% 0.13/0.63 % Net memory used: 71.454 MB
%------------------------------------------------------------------------------