%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET666+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 : 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 : Fri Sep 25 02:43:45 PM UTC 2026
% Result : Theorem 24.80s 3.68s
% Output : Proof 24.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 69 ( 10 unt; 0 def)
% Number of atoms : 247 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 298 ( 120 ~; 124 |; 27 &)
% ( 5 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 128 ( 2 sgn 59 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,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/sandbox/benchmark/theBenchmark.p',p14) ).
fof(f13_nnf,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)],[f13]) ).
fof(f13_sk,plain,
! [B,C,D] :
( ( ( ( ~ member(sk4(B,C),C)
& member(sk4(B,C),B)
& ilf_type(sk4(B,C),set_type) )
| subset(B,C) )
& ( 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(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f13_nnf]) ).
cnf(c20,plain,
( 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(esa)],[f13_sk]) ).
fof(f23,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
fof(f23_nnf,plain,
! [B] : ilf_type(B,set_type),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [B] : ilf_type(B,set_type),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c45,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p126,plain,
( member(X2,X0)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c20,c45]) ).
cnf(p265,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[p126,c45]) ).
fof(f2,axiom,
! [B] :
( ilf_type(B,set_type)
=> subset(identity_relation_of(B),cross_product(B,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f2_nnf,plain,
! [B] :
( subset(identity_relation_of(B),cross_product(B,B))
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B] :
( subset(identity_relation_of(B),cross_product(B,B))
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c3,plain,
( subset(identity_relation_of(X0),cross_product(X0,X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p68,plain,
subset(identity_relation_of(X0),cross_product(X0,X0)),
inference(resolution,[status(thm)],[c3,c45]) ).
cnf(p294,plain,
( member(X0,cross_product(X1,X1))
| ~ member(X0,identity_relation_of(X1))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p265,p68]) ).
cnf(p296,plain,
( member(X0,cross_product(X1,X1))
| ~ member(X0,identity_relation_of(X1)) ),
inference(resolution,[status(thm)],[p294,c45]) ).
fof(f15,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',p16) ).
fof(f15_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)],[f15]) ).
fof(f15_sk,plain,
! [B,C,D] :
( ( ( ( ~ member(sk5(B,C),C)
& member(sk5(B,C),B)
& ilf_type(sk5(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,[sk5])],[f15_nnf]) ).
cnf(c27,plain,
( member(sk5(X0,X1),X0)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p168,plain,
( member(sk5(X1,X0),X1)
| member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c27,c45]) ).
cnf(p175,plain,
( member(sk5(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[p168,c45]) ).
cnf(p301,plain,
( member(identity_relation_of(X0),power_set(X1))
| member(sk5(identity_relation_of(X0),X1),cross_product(X0,X0)) ),
inference(resolution,[status(thm)],[p296,p175]) ).
cnf(c28,plain,
( ~ member(sk5(X0,X1),X1)
| member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p172,plain,
( ~ member(sk5(X1,X0),X0)
| member(X1,power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c28,c45]) ).
cnf(p180,plain,
( ~ member(sk5(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[p172,c45]) ).
cnf(p334,plain,
( member(identity_relation_of(X0),power_set(cross_product(X0,X0)))
| member(identity_relation_of(X0),power_set(cross_product(X0,X0))) ),
inference(resolution,[status(thm)],[p301,p180]) ).
cnf(p350,plain,
member(identity_relation_of(X0),power_set(cross_product(X0,X0))),
inference(factoring,[status(thm)],[p334]) ).
fof(f17,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',p18) ).
fof(f17_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)],[f17]) ).
fof(f17_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)],[f17_nnf]) ).
cnf(c32,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)],[f17_sk]) ).
cnf(p185,plain,
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(resolution,[status(thm)],[c32,c45]) ).
cnf(p194,plain,
( ~ member(X1,X0)
| ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[p185,c45]) ).
cnf(p351,plain,
( ilf_type(identity_relation_of(X0),member_type(power_set(cross_product(X0,X0))))
| empty(power_set(cross_product(X0,X0))) ),
inference(resolution,[status(thm)],[p350,p194]) ).
fof(f11,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',p12) ).
fof(f11_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)],[f11]) ).
fof(f11_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)],[f11_nnf]) ).
cnf(c18,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)],[f11_sk]) ).
cnf(p119,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c18,c45]) ).
cnf(p128,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1)) ),
inference(resolution,[status(thm)],[p119,c45]) ).
cnf(p358,plain,
( ilf_type(identity_relation_of(X0),subset_type(cross_product(X0,X0)))
| empty(power_set(cross_product(X0,X0))) ),
inference(resolution,[status(thm)],[p351,p128]) ).
fof(f0,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',p1) ).
fof(f0_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)],[f0]) ).
fof(f0_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)],[f0_nnf]) ).
cnf(c0,plain,
( 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(esa)],[f0_sk]) ).
cnf(p50,plain,
( ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c0,c45]) ).
cnf(p131,plain,
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[p50,c45]) ).
cnf(p359,plain,
( ilf_type(identity_relation_of(X0),relation_type(X0,X0))
| empty(power_set(cross_product(X0,X0))) ),
inference(resolution,[status(thm)],[p358,p131]) ).
fof(f5,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,identity_relation_of_type(B))
<=> ilf_type(C,relation_type(B,B)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
fof(f5_nnf,plain,
! [B] :
( ! [C] :
( ( ( ~ ilf_type(C,relation_type(B,B))
| ilf_type(C,identity_relation_of_type(B)) )
& ( ilf_type(C,relation_type(B,B))
| ~ ilf_type(C,identity_relation_of_type(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [B,C] :
( ( ( ~ ilf_type(C,relation_type(B,B))
| ilf_type(C,identity_relation_of_type(B)) )
& ( ilf_type(C,relation_type(B,B))
| ~ ilf_type(C,identity_relation_of_type(B)) ) )
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c9,plain,
( ~ ilf_type(X1,relation_type(X0,X0))
| ilf_type(X1,identity_relation_of_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p104,plain,
( ~ ilf_type(X0,relation_type(X1,X1))
| ilf_type(X0,identity_relation_of_type(X1))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c9,c45]) ).
cnf(p115,plain,
( ~ ilf_type(X0,relation_type(X1,X1))
| ilf_type(X0,identity_relation_of_type(X1)) ),
inference(resolution,[status(thm)],[p104,c45]) ).
cnf(p360,plain,
( ilf_type(identity_relation_of(X0),identity_relation_of_type(X0))
| empty(power_set(cross_product(X0,X0))) ),
inference(resolution,[status(thm)],[p359,p115]) ).
fof(f16,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',p17) ).
fof(f16_nnf,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c29,plain,
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p54,plain,
~ empty(power_set(X0)),
inference(resolution,[status(thm)],[c29,c45]) ).
cnf(p363,plain,
ilf_type(identity_relation_of(X0),identity_relation_of_type(X0)),
inference(resolution,[status(thm)],[p360,p54]) ).
fof(f24,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ilf_type(identity_relation_of(B),identity_relation_of_type(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_29) ).
fof(f24_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ilf_type(identity_relation_of(B),identity_relation_of_type(B)) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f24_nnf,plain,
? [B] :
( ~ ilf_type(identity_relation_of(B),identity_relation_of_type(B))
& ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f24_neg]) ).
fof(f24_sk,plain,
( ~ ilf_type(identity_relation_of(sk11),identity_relation_of_type(sk11))
& ilf_type(sk11,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f24_nnf]) ).
cnf(c47,plain,
~ ilf_type(identity_relation_of(sk11),identity_relation_of_type(sk11)),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p364,plain,
$false,
inference(resolution,[status(thm)],[p363,c47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET666+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Thu Sep 24 11:41:42 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 24.80/3.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.80/3.68 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------