%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET663+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 8.31s 1.65s
% Output : Proof 8.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 72 ( 32 unt; 0 def)
% Number of atoms : 199 ( 42 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 214 ( 87 ~; 70 |; 28 &)
% ( 2 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-4 aty)
% Number of variables : 94 ( 2 sgn 60 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(range_of(D),C)
& subset(domain_of(D),B) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f2_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( subset(range_of(D),C)
& subset(domain_of(D),B) )
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,C,D] :
( ( subset(range_of(D),C)
& subset(domain_of(D),B) )
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c3,plain,
( subset(domain_of(X2),X0)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi3,axiom,
ifeq(ilf_type(X0,set_type),true,ifeq(ilf_type(X1,set_type),true,ifeq(ilf_type(X2,relation_type(X0,X1)),true,subset(domain_of(X2),X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
fof(f33,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p33) ).
fof(f33_nnf,plain,
! [B] : ilf_type(B,set_type),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [B] : ilf_type(B,set_type),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c61,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(hi54,axiom,
ilf_type(X0,set_type) = true,
inference(equality_encoding,[status(esa)],[c61]) ).
fof(f34,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( ilf_type(D,relation_type(empty_set,C))
=> D = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_26) ).
fof(f34_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( ilf_type(D,relation_type(empty_set,C))
=> D = empty_set ) ) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f34_nnf,plain,
? [B] :
( ? [C] :
( ? [D] :
( D != empty_set
& ilf_type(D,relation_type(empty_set,C))
& ilf_type(D,relation_type(B,C)) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f34_neg]) ).
fof(f34_sk,plain,
( sk14 != empty_set
& ilf_type(sk14,relation_type(empty_set,sk13))
& ilf_type(sk14,relation_type(sk12,sk13))
& ilf_type(sk13,set_type)
& ilf_type(sk12,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12,sk13,sk14])],[f34_nnf]) ).
cnf(c63,plain,
ilf_type(sk13,set_type),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(hi56,negated_conjecture,
ilf_type(sk13,set_type) = true,
inference(equality_encoding,[status(esa)],[c63]) ).
cnf(c65,plain,
ilf_type(sk14,relation_type(empty_set,sk13)),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(hi58,negated_conjecture,
ilf_type(sk14,relation_type(empty_set,sk13)) = true,
inference(equality_encoding,[status(esa)],[c65]) ).
cnf(h35,plain,
subset(domain_of(sk14),empty_set) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi54,hi56,hi58]) ).
fof(f0,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( subset(B,empty_set)
=> B = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f0_nnf,plain,
! [B] :
( B = empty_set
| ~ subset(B,empty_set)
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B] :
( B = empty_set
| ~ subset(B,empty_set)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( X0 = empty_set
| ~ subset(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(ilf_type(X0,set_type),true,ifeq(subset(X0,empty_set),true,X0,empty_set),empty_set) = empty_set,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h36,plain,
domain_of(sk14) = empty_set,
inference(hyper_resolution,[status(thm)],[hi0,hi54,h35]) ).
fof(f6,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',p6) ).
fof(f6_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)],[f6]) ).
fof(f6_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)],[f6_nnf]) ).
cnf(c9,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)],[f6_sk]) ).
cnf(hi8,axiom,
ifeq(ilf_type(X0,set_type),true,ifeq(ilf_type(X1,set_type),true,ifeq(ilf_type(X2,relation_type(X0,X1)),true,ilf_type(X2,subset_type(cross_product(X0,X1))),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(c62,plain,
ilf_type(sk12,set_type),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(hi55,negated_conjecture,
ilf_type(sk12,set_type) = true,
inference(equality_encoding,[status(esa)],[c62]) ).
cnf(c64,plain,
ilf_type(sk14,relation_type(sk12,sk13)),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(hi57,negated_conjecture,
ilf_type(sk14,relation_type(sk12,sk13)) = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(h27,plain,
ilf_type(sk14,subset_type(cross_product(sk12,sk13))) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi55,hi56,hi57]) ).
fof(f28,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',p28) ).
fof(f28_nnf,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(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,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(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c56,plain,
( 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(esa)],[f28_sk]) ).
cnf(hi49,axiom,
ifeq(ilf_type(X0,set_type),true,ifeq(ilf_type(X1,set_type),true,ifeq(ilf_type(X2,subset_type(cross_product(X0,X1))),true,relation_like(X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(h59,plain,
relation_like(sk14) = true,
inference(hyper_resolution,[status(thm)],[hi49,hi55,hi56,h27]) ).
fof(f13,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',p13) ).
fof(f13_nnf,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)],[f13]) ).
fof(f13_sk,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(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c25,plain,
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi21,axiom,
ifeq(ilf_type(X0,set_type),true,ifeq(relation_like(X0),true,ifeq(ilf_type(X0,set_type),true,ilf_type(X0,binary_relation_type),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(h61,plain,
ilf_type(sk14,binary_relation_type) = true,
inference(hyper_resolution,[status(thm)],[hi21,hi54,h59,hi54]) ).
fof(f1,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ( ( range_of(B) = empty_set
| domain_of(B) = empty_set )
=> B = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f1_nnf,plain,
! [B] :
( B = empty_set
| ( range_of(B) != empty_set
& domain_of(B) != empty_set )
| ~ ilf_type(B,binary_relation_type) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B] :
( B = empty_set
| ( range_of(B) != empty_set
& domain_of(B) != empty_set )
| ~ ilf_type(B,binary_relation_type) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( X0 = empty_set
| domain_of(X0) != empty_set
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(ilf_type(X0,binary_relation_type),true,ifeq(domain_of(X0),empty_set,X0,empty_set),empty_set) = empty_set,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h72,plain,
sk14 = empty_set,
inference(hyper_resolution,[status(thm)],[hi1,h61,h36]) ).
cnf(c66,plain,
sk14 != empty_set,
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(hi62,negated_conjecture,
ifeq(sk14,empty_set,false,true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t1,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi62,h72]) ).
cnf(t346,plain,
false = true,
inference(orient,[status(thm)],[t1]) ).
fof(f3,axiom,
! [B] :
( ilf_type(B,set_type)
=> ~ member(B,empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(f3_nnf,plain,
! [B] :
( ~ member(B,empty_set)
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B] :
( ~ member(B,empty_set)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c5,plain,
( ~ member(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f21,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
fof(f21_nnf,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)],[f21]) ).
fof(f21_sk,plain,
! [B,C] :
( ( ( ( member(sk6(B),B)
& ilf_type(sk6(B),set_type) )
| empty(B) )
& ( ~ member(C,B)
| ~ ilf_type(C,set_type)
| ~ empty(B) ) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk6])],[f21_nnf]) ).
cnf(c37,plain,
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
fof(f23,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',p23) ).
fof(f23_nnf,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c44,plain,
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c5,c37,c44,c66]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t346]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET663+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 11:40:45 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.31/1.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.31/1.65 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------