%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET659+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 02:43:44 PM UTC 2026
% Result : Theorem 22.28s 13.23s
% Output : Proof 22.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 15
% Syntax : Number of formulae : 134 ( 18 unt; 0 def)
% Number of atoms : 515 ( 37 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 630 ( 249 ~; 268 |; 59 &)
% ( 9 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-3 aty)
% Number of variables : 248 ( 8 sgn 113 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f30,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(domain(B,C,D),subset_type(B)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p31) ).
fof(f30_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( ilf_type(domain(B,C,D),subset_type(B))
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [B,C,D] :
( ilf_type(domain(B,C,D),subset_type(B))
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c65,plain,
( ilf_type(domain(X0,X1,X2),subset_type(X0))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f33,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p34) ).
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(c68,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(p411,plain,
( ilf_type(domain(X2,X0,X1),subset_type(X2))
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c65,c68]) ).
cnf(p702,plain,
( ilf_type(domain(X1,X2,X0),subset_type(X1))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p411,c68]) ).
fof(f34,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( ! [E] :
( ilf_type(E,set_type)
=> ( member(E,C)
=> ? [F] :
( member(ordered_pair(E,F),D)
& ilf_type(F,set_type) ) ) )
<=> domain(C,B,D) = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_22) ).
fof(f34_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( ! [E] :
( ilf_type(E,set_type)
=> ( member(E,C)
=> ? [F] :
( member(ordered_pair(E,F),D)
& ilf_type(F,set_type) ) ) )
<=> domain(C,B,D) = C ) ) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f34_nnf,plain,
? [B] :
( ? [C] :
( ? [D] :
( ( ( domain(C,B,D) = C
& ? [E] :
( ! [F] :
( ~ member(ordered_pair(E,F),D)
| ~ ilf_type(F,set_type) )
& member(E,C)
& ilf_type(E,set_type) ) )
| ( domain(C,B,D) != C
& ! [E] :
( ? [F] :
( member(ordered_pair(E,F),D)
& ilf_type(F,set_type) )
| ~ member(E,C)
| ~ ilf_type(E,set_type) ) ) )
& ilf_type(D,relation_type(C,B)) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f34_neg]) ).
fof(f34_sk,plain,
! [E,F] :
( ( ( domain(sk14,sk13,sk15) = sk14
& ( ~ member(ordered_pair(sk17,F),sk15)
| ~ ilf_type(F,set_type) )
& member(sk17,sk14)
& ilf_type(sk17,set_type) )
| ( domain(sk14,sk13,sk15) != sk14
& ( ( member(ordered_pair(E,sk16(E)),sk15)
& ilf_type(sk16(E),set_type) )
| ~ member(E,sk14)
| ~ ilf_type(E,set_type) ) ) )
& ilf_type(sk15,relation_type(sk14,sk13))
& ilf_type(sk14,set_type)
& ilf_type(sk13,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13,sk14,sk15,sk16,sk17])],[f34_nnf]) ).
cnf(c71,plain,
ilf_type(sk15,relation_type(sk14,sk13)),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p2167,plain,
ilf_type(domain_of(sk15),subset_type(sk14)),
inference(resolution,[status(thm)],[p702,c71]) ).
fof(f16,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',p17) ).
fof(f16_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)],[f16]) ).
fof(f16_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)],[f16_nnf]) ).
cnf(c29,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)],[f16_sk]) ).
cnf(p223,plain,
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c29,c68]) ).
cnf(p254,plain,
( ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,subset_type(X1)) ),
inference(resolution,[status(thm)],[p223,c68]) ).
cnf(p2171,plain,
ilf_type(domain_of(sk15),member_type(power_set(sk14))),
inference(resolution,[status(thm)],[p2167,p254]) ).
fof(f23,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',p24) ).
fof(f23_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)],[f23]) ).
fof(f23_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)],[f23_nnf]) ).
cnf(c50,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)],[f23_sk]) ).
cnf(p359,plain,
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| ~ ilf_type(X0,set_type)
| empty(X0) ),
inference(resolution,[status(thm)],[c50,c68]) ).
cnf(p616,plain,
( member(X1,X0)
| ~ ilf_type(X1,member_type(X0))
| empty(X0) ),
inference(resolution,[status(thm)],[p359,c68]) ).
cnf(p2172,plain,
( member(domain_of(sk15),power_set(sk14))
| empty(power_set(sk14)) ),
inference(resolution,[status(thm)],[p2171,p616]) ).
fof(f21,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',p22) ).
fof(f21_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)],[f21]) ).
fof(f21_sk,plain,
! [B,C,D] :
( ( ( ( ~ member(sk7(B,C),C)
& member(sk7(B,C),B)
& ilf_type(sk7(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,[sk7])],[f21_nnf]) ).
cnf(c44,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)],[f21_sk]) ).
cnf(p320,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)],[c44,c68]) ).
cnf(p613,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ member(X0,power_set(X1)) ),
inference(resolution,[status(thm)],[p320,c68]) ).
cnf(p2173,plain,
( member(X0,sk14)
| ~ member(X0,domain_of(sk15))
| ~ ilf_type(X0,set_type)
| empty(power_set(sk14)) ),
inference(resolution,[status(thm)],[p2172,p613]) ).
cnf(p2260,plain,
( member(X0,sk14)
| ~ member(X0,domain_of(sk15))
| empty(power_set(sk14)) ),
inference(resolution,[status(thm)],[p2173,c68]) ).
fof(f19,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',p20) ).
fof(f19_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)],[f19]) ).
fof(f19_sk,plain,
! [B,C,D] :
( ( ( ( ~ member(sk6(B,C),C)
& member(sk6(B,C),B)
& ilf_type(sk6(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,[sk6])],[f19_nnf]) ).
cnf(c41,plain,
( member(sk6(X0,X1),X0)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p293,plain,
( member(sk6(X1,X0),X1)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c41,c68]) ).
cnf(p296,plain,
( member(sk6(X0,X1),X0)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[p293,c68]) ).
cnf(p2263,plain,
( subset(domain_of(sk15),X0)
| member(sk6(domain_of(sk15),X0),sk14)
| empty(power_set(sk14)) ),
inference(resolution,[status(thm)],[p2260,p296]) ).
cnf(c42,plain,
( ~ member(sk6(X0,X1),X1)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p311,plain,
( ~ member(sk6(X1,X0),X0)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c42,c68]) ).
cnf(p314,plain,
( ~ member(sk6(X0,X1),X1)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[p311,c68]) ).
cnf(p2298,plain,
( subset(domain_of(sk15),sk14)
| subset(domain_of(sk15),sk14)
| empty(power_set(sk14)) ),
inference(resolution,[status(thm)],[p2263,p314]) ).
cnf(p2301,plain,
( subset(domain_of(sk15),sk14)
| empty(power_set(sk14)) ),
inference(factoring,[status(thm)],[p2298]) ).
fof(f29,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> domain(B,C,D) = domain_of(D) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p30) ).
fof(f29_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( domain(B,C,D) = domain_of(D)
| ~ ilf_type(D,relation_type(B,C)) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [B,C,D] :
( domain(B,C,D) = domain_of(D)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c64,plain,
( domain(X0,X1,X2) = domain_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p398,plain,
( domain(X2,X0,X1) = domain_of(X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c64,c68]) ).
cnf(p684,plain,
( domain(X1,X2,X0) = domain_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p398,c68]) ).
cnf(p1797,plain,
domain(sk14,sk13,sk15) = domain_of(sk15),
inference(resolution,[status(thm)],[p684,c71]) ).
fof(f2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,binary_relation_type)
=> ( member(ordered_pair(B,C),D)
=> ( member(C,range_of(D))
& member(B,domain_of(D)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f2_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( ( member(C,range_of(D))
& member(B,domain_of(D)) )
| ~ member(ordered_pair(B,C),D)
| ~ ilf_type(D,binary_relation_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,C,D] :
( ( member(C,range_of(D))
& member(B,domain_of(D)) )
| ~ member(ordered_pair(B,C),D)
| ~ ilf_type(D,binary_relation_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c4,plain,
( member(X0,domain_of(X2))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p136,plain,
( member(X2,domain_of(X1))
| ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c68,c4]) ).
cnf(p442,plain,
( member(X1,domain_of(X0))
| ~ member(ordered_pair(X1,X2),X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[p136,c68]) ).
fof(f26,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',p27) ).
fof(f26_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)],[f26]) ).
fof(f26_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)],[f26_nnf]) ).
cnf(c59,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)],[f26_sk]) ).
cnf(p324,plain,
( relation_like(X1)
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c59,c68]) ).
cnf(p327,plain,
( relation_like(X0)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[p324,c68]) ).
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',p7) ).
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(c15,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(p159,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)],[c15,c68]) ).
cnf(p283,plain,
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p159,c68]) ).
cnf(p284,plain,
ilf_type(sk15,subset_type(cross_product(sk14,sk13))),
inference(resolution,[status(thm)],[p283,c71]) ).
cnf(p330,plain,
relation_like(sk15),
inference(resolution,[status(thm)],[p327,p284]) ).
fof(f14,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',p15) ).
fof(f14_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)],[f14]) ).
fof(f14_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)],[f14_nnf]) ).
cnf(c27,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)],[f14_sk]) ).
cnf(p213,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(factoring,[status(thm)],[c27]) ).
cnf(p216,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[p213,c68]) ).
cnf(p332,plain,
ilf_type(sk15,binary_relation_type),
inference(resolution,[status(thm)],[p330,p216]) ).
cnf(p446,plain,
( member(X0,domain_of(sk15))
| ~ member(ordered_pair(X0,X1),sk15) ),
inference(resolution,[status(thm)],[p442,p332]) ).
cnf(c79,plain,
( domain(sk14,sk13,sk15) = sk14
| member(ordered_pair(X3,sk16(X3)),sk15)
| ~ member(X3,sk14)
| ~ ilf_type(X3,set_type) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p135,plain,
( domain(sk14,sk13,sk15) = sk14
| member(ordered_pair(X0,sk16(X0)),sk15)
| ~ member(X0,sk14) ),
inference(resolution,[status(thm)],[c68,c79]) ).
cnf(p298,plain,
( domain(sk14,sk13,sk15) = sk14
| member(ordered_pair(sk6(sk14,X0),sk16(sk6(sk14,X0))),sk15)
| subset(sk14,X0) ),
inference(resolution,[status(thm)],[p296,p135]) ).
cnf(p459,plain,
( domain(sk14,sk13,sk15) = sk14
| subset(sk14,X0)
| member(sk6(sk14,X0),domain_of(sk15)) ),
inference(resolution,[status(thm)],[p446,p298]) ).
cnf(p496,plain,
( subset(sk14,domain_of(sk15))
| domain(sk14,sk13,sk15) = sk14
| subset(sk14,domain_of(sk15)) ),
inference(resolution,[status(thm)],[p459,p314]) ).
cnf(p498,plain,
( domain(sk14,sk13,sk15) = sk14
| subset(sk14,domain_of(sk15)) ),
inference(factoring,[status(thm)],[p496]) ).
fof(f8,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( B = C
<=> ( subset(C,B)
& subset(B,C) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9) ).
fof(f8_nnf,plain,
! [B] :
( ! [C] :
( ( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [B,C] :
( ( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) )
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c18,plain,
( subset(X1,X0)
| X0 != X1
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p181,plain,
( subset(X0,X1)
| X1 != X0
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c18,c68]) ).
cnf(p219,plain,
( subset(X1,X0)
| X0 != X1 ),
inference(resolution,[status(thm)],[p181,c68]) ).
cnf(p501,plain,
( subset(sk14,domain(sk14,sk13,sk15))
| subset(sk14,domain_of(sk15)) ),
inference(resolution,[status(thm)],[p498,p219]) ).
cnf(p1818,plain,
( subset(sk14,domain_of(sk15))
| subset(sk14,domain_of(sk15)) ),
inference(demodulation,[status(thm)],[p1797,p501]) ).
cnf(p2137,plain,
subset(sk14,domain_of(sk15)),
inference(factoring,[status(thm)],[p1818]) ).
cnf(c19,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p185,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X1 = X0
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c19,c68]) ).
cnf(p267,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[p185,c68]) ).
cnf(p2138,plain,
( ~ subset(domain_of(sk15),sk14)
| sk14 = domain_of(sk15) ),
inference(resolution,[status(thm)],[p2137,p267]) ).
cnf(p2303,plain,
( sk14 = domain_of(sk15)
| empty(power_set(sk14)) ),
inference(resolution,[status(thm)],[p2301,p2138]) ).
cnf(p2369,plain,
( domain_of(sk15) = sk14
| empty(power_set(sk14)) ),
inference(superposition,[status(thm)],[p2303,p1797]) ).
cnf(c82,plain,
( ~ member(ordered_pair(sk17,X4),sk15)
| ~ ilf_type(X4,set_type)
| domain(sk14,sk13,sk15) != sk14 ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p1799,plain,
( ~ member(ordered_pair(sk17,X0),sk15)
| ~ ilf_type(X0,set_type)
| domain_of(sk15) != sk14 ),
inference(demodulation,[status(thm)],[p1797,c82]) ).
cnf(p2383,plain,
( ~ member(ordered_pair(sk17,X0),sk15)
| ~ ilf_type(X0,set_type)
| empty(power_set(sk14)) ),
inference(resolution,[status(thm)],[p2369,p1799]) ).
cnf(p2432,plain,
( ~ member(ordered_pair(sk17,X0),sk15)
| empty(power_set(sk14)) ),
inference(resolution,[status(thm)],[p2383,c68]) ).
cnf(c81,plain,
( member(sk17,sk14)
| domain(sk14,sk13,sk15) != sk14 ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(p1798,plain,
( member(sk17,sk14)
| domain_of(sk15) != sk14 ),
inference(demodulation,[status(thm)],[p1797,c81]) ).
cnf(p2382,plain,
( member(sk17,sk14)
| empty(power_set(sk14)) ),
inference(resolution,[status(thm)],[p2369,p1798]) ).
fof(f22,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(f22_nnf,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [B] :
( ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) )
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c48,plain,
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p165,plain,
~ empty(power_set(X0)),
inference(resolution,[status(thm)],[c48,c68]) ).
cnf(p2384,plain,
member(sk17,sk14),
inference(resolution,[status(thm)],[p2382,p165]) ).
cnf(c39,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)],[f19_sk]) ).
cnf(p305,plain,
( member(X2,X0)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c39,c68]) ).
cnf(p571,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[p305,c68]) ).
cnf(p2139,plain,
( member(X0,domain_of(sk15))
| ~ member(X0,sk14)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p2137,p571]) ).
cnf(p2181,plain,
( member(X0,domain_of(sk15))
| ~ member(X0,sk14) ),
inference(resolution,[status(thm)],[p2139,c68]) ).
cnf(p2387,plain,
member(sk17,domain_of(sk15)),
inference(resolution,[status(thm)],[p2384,p2181]) ).
fof(f0,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(C,domain_of(B))
<=> ? [D] :
( member(ordered_pair(C,D),B)
& ilf_type(D,set_type) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f0_nnf,plain,
! [B] :
( ! [C] :
( ( ( ! [D] :
( ~ member(ordered_pair(C,D),B)
| ~ ilf_type(D,set_type) )
| member(C,domain_of(B)) )
& ( ? [D] :
( member(ordered_pair(C,D),B)
& ilf_type(D,set_type) )
| ~ member(C,domain_of(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,binary_relation_type) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C,D] :
( ( ( ~ member(ordered_pair(C,D),B)
| ~ ilf_type(D,set_type)
| member(C,domain_of(B)) )
& ( ( member(ordered_pair(C,sk0(B,C)),B)
& ilf_type(sk0(B,C),set_type) )
| ~ member(C,domain_of(B)) ) )
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,binary_relation_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c1,plain,
( member(ordered_pair(X1,sk0(X0,X1)),X0)
| ~ member(X1,domain_of(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p333,plain,
( member(ordered_pair(X0,sk0(sk15,X0)),sk15)
| ~ member(X0,domain_of(sk15))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p332,c1]) ).
cnf(p352,plain,
( member(ordered_pair(X0,sk0(sk15,X0)),sk15)
| ~ member(X0,domain_of(sk15)) ),
inference(resolution,[status(thm)],[p333,c68]) ).
cnf(p2389,plain,
member(ordered_pair(sk17,sk0(sk15,sk17)),sk15),
inference(resolution,[status(thm)],[p2387,p352]) ).
cnf(p2439,plain,
empty(power_set(sk14)),
inference(resolution,[status(thm)],[p2432,p2389]) ).
cnf(p2440,plain,
$false,
inference(resolution,[status(thm)],[p2439,p165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET659+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/10.38 % Computer : n016.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Thu Sep 24 11:40:24 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 22.28/13.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.28/13.23 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------