%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET645+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 : Fri Sep 25 02:43:42 PM UTC 2026
% Result : Theorem 23.14s 3.83s
% Output : Proof 23.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 65 ( 13 unt; 0 def)
% Number of atoms : 264 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 329 ( 130 ~; 130 |; 36 &)
% ( 4 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 142 ( 12 sgn 61 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,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',p13) ).
fof(f12_nnf,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)],[f12]) ).
fof(f12_sk,plain,
! [B,C,D] :
( ( ( ( ~ member(sk3(B,C),C)
& member(sk3(B,C),B)
& ilf_type(sk3(B,C),set_type) )
| member(B,power_set(C)) )
& ( 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(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f12_nnf]) ).
cnf(c23,plain,
( 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(esa)],[f12_sk]) ).
fof(f20,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
fof(f20_nnf,plain,
! [B] : ilf_type(B,set_type),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [B] : ilf_type(B,set_type),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c43,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p150,plain,
( member(X2,X0)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c23,c43]) ).
cnf(p300,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[p150,c43]) ).
fof(f14,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',p15) ).
fof(f14_nnf,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)],[f14]) ).
fof(f14_sk,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(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c29,plain,
( 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(esa)],[f14_sk]) ).
cnf(p145,plain,
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(resolution,[status(thm)],[c29,c43]) ).
cnf(p146,plain,
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[p145,c43]) ).
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/sandbox/benchmark/theBenchmark.p',p4) ).
fof(f3_nnf,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(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,C,D,E] :
( ( ( ilf_type(E,subset_type(cross_product(B,C)))
| ~ ilf_type(E,relation_type(B,C)) )
& ( 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(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c7,plain,
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p91,plain,
( ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c7,c43]) ).
cnf(p122,plain,
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p91,c43]) ).
fof(f21,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/sandbox/benchmark/theBenchmark.p',prove_relset_1_7) ).
fof(f21_neg,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)],[f21]) ).
fof(f21_nnf,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(nnf_transformation,[status(thm)],[f21_neg]) ).
fof(f21_sk,plain,
( ( ~ member(sk12,sk10)
| ~ member(sk11,sk9) )
& member(ordered_pair(sk11,sk12),sk13)
& ilf_type(sk13,relation_type(sk9,sk10))
& ilf_type(sk12,set_type)
& ilf_type(sk11,set_type)
& ilf_type(sk10,set_type)
& ilf_type(sk9,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9,sk10,sk11,sk12,sk13])],[f21_nnf]) ).
cnf(c48,plain,
ilf_type(sk13,relation_type(sk9,sk10)),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p123,plain,
ilf_type(sk13,subset_type(cross_product(sk9,sk10))),
inference(resolution,[status(thm)],[p122,c48]) ).
fof(f9,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',p10) ).
fof(f9_nnf,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)],[f9]) ).
fof(f9_sk,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(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c13,plain,
( 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(esa)],[f9_sk]) ).
cnf(p97,plain,
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c13,c43]) ).
cnf(p107,plain,
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(resolution,[status(thm)],[p97,c43]) ).
cnf(p125,plain,
ilf_type(sk13,member_type(power_set(cross_product(sk9,sk10)))),
inference(resolution,[status(thm)],[p123,p107]) ).
cnf(p153,plain,
( member(sk13,power_set(cross_product(sk9,sk10)))
| empty(power_set(cross_product(sk9,sk10))) ),
inference(resolution,[status(thm)],[p146,p125]) ).
cnf(p307,plain,
( empty(power_set(cross_product(sk9,sk10)))
| member(X0,cross_product(sk9,sk10))
| ~ member(X0,sk13)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p300,p153]) ).
cnf(p565,plain,
( empty(power_set(cross_product(sk9,sk10)))
| member(X0,cross_product(sk9,sk10))
| ~ member(X0,sk13) ),
inference(resolution,[status(thm)],[p307,c43]) ).
cnf(c49,plain,
member(ordered_pair(sk11,sk12),sk13),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p566,plain,
( empty(power_set(cross_product(sk9,sk10)))
| member(ordered_pair(sk11,sk12),cross_product(sk9,sk10)) ),
inference(resolution,[status(thm)],[p565,c49]) ).
fof(f0,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',p1) ).
fof(f0_nnf,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)],[f0]) ).
fof(f0_sk,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(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c1,plain,
( 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(esa)],[f0_sk]) ).
cnf(p65,plain,
( 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(resolution,[status(thm)],[c1,c43]) ).
cnf(p240,plain,
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p65,c43]) ).
cnf(p536,plain,
( member(X2,X0)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p240,c43]) ).
cnf(p538,plain,
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(resolution,[status(thm)],[p536,c43]) ).
cnf(p593,plain,
( member(sk12,sk10)
| empty(power_set(cross_product(sk9,sk10))) ),
inference(resolution,[status(thm)],[p566,p538]) ).
fof(f13,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',p14) ).
fof(f13_nnf,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c27,plain,
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p58,plain,
~ empty(power_set(X0)),
inference(resolution,[status(thm)],[c27,c43]) ).
cnf(p599,plain,
member(sk12,sk10),
inference(resolution,[status(thm)],[p593,p58]) ).
cnf(c0,plain,
( 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(esa)],[f0_sk]) ).
cnf(p57,plain,
( 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(resolution,[status(thm)],[c0,c43]) ).
cnf(p204,plain,
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p57,c43]) ).
cnf(p280,plain,
( member(X1,X3)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p204,c43]) ).
cnf(p285,plain,
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(resolution,[status(thm)],[p280,c43]) ).
cnf(p591,plain,
( member(sk11,sk9)
| empty(power_set(cross_product(sk9,sk10))) ),
inference(resolution,[status(thm)],[p566,p285]) ).
cnf(p595,plain,
member(sk11,sk9),
inference(resolution,[status(thm)],[p591,p58]) ).
cnf(c50,plain,
( ~ member(sk12,sk10)
| ~ member(sk11,sk9) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p597,plain,
~ member(sk12,sk10),
inference(resolution,[status(thm)],[p595,c50]) ).
cnf(p602,plain,
$false,
inference(resolution,[status(thm)],[p599,p597]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET645+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 11:33:48 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 23.14/3.83 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.14/3.83 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------