%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET667+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 29.34s 4.76s
% Output : Proof 29.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 89 ( 16 unt; 0 def)
% Number of atoms : 312 ( 14 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 376 ( 153 ~; 155 |; 31 &)
% ( 3 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 178 ( 9 sgn 77 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> range(B,C,D) = range_of(D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p29) ).
fof(f28_nnf,plain,
! [B] :
( ! [C] :
( ! [D] :
( range(B,C,D) = range_of(D)
| ~ ilf_type(D,relation_type(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] :
( range(B,C,D) = range_of(D)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c55,plain,
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
fof(f30,axiom,
! [B] : ilf_type(B,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p31) ).
fof(f30_nnf,plain,
! [B] : ilf_type(B,set_type),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [B] : ilf_type(B,set_type),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c57,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(p273,plain,
( range(X2,X0,X1) = range_of(X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c55,c57]) ).
cnf(p1722,plain,
( range(X1,X2,X0) = range_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p273,c57]) ).
fof(f31,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,C))
=> ( subset(identity_relation_of(D),E)
=> ( subset(D,range(B,C,E))
& subset(D,domain(B,C,E)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_30) ).
fof(f31_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,relation_type(B,C))
=> ( subset(identity_relation_of(D),E)
=> ( subset(D,range(B,C,E))
& subset(D,domain(B,C,E)) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f31_nnf,plain,
? [B] :
( ? [C] :
( ? [D] :
( ? [E] :
( ( ~ subset(D,range(B,C,E))
| ~ subset(D,domain(B,C,E)) )
& subset(identity_relation_of(D),E)
& ilf_type(E,relation_type(B,C)) )
& ilf_type(D,set_type) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f31_neg]) ).
fof(f31_sk,plain,
( ( ~ subset(sk14,range(sk12,sk13,sk15))
| ~ subset(sk14,domain(sk12,sk13,sk15)) )
& subset(identity_relation_of(sk14),sk15)
& ilf_type(sk15,relation_type(sk12,sk13))
& ilf_type(sk14,set_type)
& ilf_type(sk13,set_type)
& ilf_type(sk12,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12,sk13,sk14,sk15])],[f31_nnf]) ).
cnf(c61,plain,
ilf_type(sk15,relation_type(sk12,sk13)),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p2637,plain,
range(sk12,sk13,sk15) = range_of(sk15),
inference(resolution,[status(thm)],[p1722,c61]) ).
fof(f26,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/sandbox2/benchmark/theBenchmark.p',p27) ).
fof(f26_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)],[f26]) ).
fof(f26_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)],[f26_nnf]) ).
cnf(c53,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)],[f26_sk]) ).
cnf(p257,plain,
( domain(X2,X0,X1) = domain_of(X1)
| ~ ilf_type(X1,relation_type(X2,X0))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c53,c57]) ).
cnf(p1126,plain,
( domain(X1,X2,X0) = domain_of(X0)
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p257,c57]) ).
cnf(p2078,plain,
domain(sk12,sk13,sk15) = domain_of(sk15),
inference(resolution,[status(thm)],[p1126,c61]) ).
cnf(c63,plain,
( ~ subset(sk14,range(sk12,sk13,sk15))
| ~ subset(sk14,domain(sk12,sk13,sk15)) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p2079,plain,
( ~ subset(sk14,range(sk12,sk13,sk15))
| ~ subset(sk14,domain_of(sk15)) ),
inference(demodulation,[status(thm)],[p2078,c63]) ).
fof(f6,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/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(f6_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)],[f6]) ).
fof(f6_sk,plain,
! [B,C,D] :
( ( ( ( ~ member(sk1(B,C),C)
& member(sk1(B,C),B)
& ilf_type(sk1(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,[sk1])],[f6_nnf]) ).
cnf(c11,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)],[f6_sk]) ).
cnf(p107,plain,
( member(X2,X0)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c11,c57]) ).
cnf(p352,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ subset(X0,X1) ),
inference(resolution,[status(thm)],[p107,c57]) ).
cnf(c62,plain,
subset(identity_relation_of(sk14),sk15),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p963,plain,
( member(X0,sk15)
| ~ member(X0,identity_relation_of(sk14))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[p352,c62]) ).
cnf(p966,plain,
( member(X0,sk15)
| ~ member(X0,identity_relation_of(sk14)) ),
inference(resolution,[status(thm)],[p963,c57]) ).
cnf(c13,plain,
( member(sk1(X0,X1),X0)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p114,plain,
( member(sk1(X1,X0),X1)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c13,c57]) ).
cnf(p117,plain,
( member(sk1(X0,X1),X0)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[p114,c57]) ).
fof(f1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(C,B)
<=> member(ordered_pair(C,C),identity_relation_of(B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f1_nnf,plain,
! [B] :
( ! [C] :
( ( ( ~ member(ordered_pair(C,C),identity_relation_of(B))
| member(C,B) )
& ( member(ordered_pair(C,C),identity_relation_of(B))
| ~ member(C,B) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C] :
( ( ( ~ member(ordered_pair(C,C),identity_relation_of(B))
| member(C,B) )
& ( member(ordered_pair(C,C),identity_relation_of(B))
| ~ member(C,B) ) )
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c2,plain,
( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p72,plain,
( member(ordered_pair(X0,X0),identity_relation_of(X1))
| ~ member(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c2,c57]) ).
cnf(p102,plain,
( member(ordered_pair(X0,X0),identity_relation_of(X1))
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[p72,c57]) ).
cnf(p119,plain,
( member(ordered_pair(sk1(X0,X1),sk1(X0,X1)),identity_relation_of(X0))
| subset(X0,X1) ),
inference(resolution,[status(thm)],[p117,p102]) ).
cnf(p971,plain,
( subset(sk14,X0)
| member(ordered_pair(sk1(sk14,X0),sk1(sk14,X0)),sk15) ),
inference(resolution,[status(thm)],[p966,p119]) ).
fof(f0,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/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f0_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)],[f0]) ).
fof(f0_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)],[f0_nnf]) ).
cnf(c0,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)],[f0_sk]) ).
cnf(p65,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)],[c0,c57]) ).
cnf(p285,plain,
( member(X1,domain_of(X0))
| ~ member(ordered_pair(X1,X2),X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[p65,c57]) ).
fof(f23,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/sandbox2/benchmark/theBenchmark.p',p24) ).
fof(f23_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)],[f23]) ).
fof(f23_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)],[f23_nnf]) ).
cnf(c48,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)],[f23_sk]) ).
cnf(p126,plain,
( relation_like(X1)
| ~ ilf_type(X1,subset_type(cross_product(X2,X0)))
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c48,c57]) ).
cnf(p127,plain,
( relation_like(X0)
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(resolution,[status(thm)],[p126,c57]) ).
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',p5) ).
fof(f4_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)],[f4]) ).
fof(f4_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)],[f4_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)],[f4_sk]) ).
cnf(p95,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)],[c9,c57]) ).
cnf(p113,plain,
( ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X0,relation_type(X1,X2)) ),
inference(resolution,[status(thm)],[p95,c57]) ).
cnf(p115,plain,
ilf_type(sk15,subset_type(cross_product(sk12,sk13))),
inference(resolution,[status(thm)],[p113,c61]) ).
cnf(p131,plain,
relation_like(sk15),
inference(resolution,[status(thm)],[p127,p115]) ).
fof(f12,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
fof(f12_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)],[f12]) ).
fof(f12_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)],[f12_nnf]) ).
cnf(c26,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)],[f12_sk]) ).
cnf(p93,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(factoring,[status(thm)],[c26]) ).
cnf(p96,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[p93,c57]) ).
cnf(p133,plain,
ilf_type(sk15,binary_relation_type),
inference(resolution,[status(thm)],[p131,p96]) ).
cnf(p288,plain,
( member(X0,domain_of(sk15))
| ~ member(ordered_pair(X0,X1),sk15) ),
inference(resolution,[status(thm)],[p285,p133]) ).
cnf(p1729,plain,
( member(sk1(sk14,X0),domain_of(sk15))
| subset(sk14,X0) ),
inference(resolution,[status(thm)],[p971,p288]) ).
cnf(c14,plain,
( ~ member(sk1(X0,X1),X1)
| subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p118,plain,
( ~ member(sk1(X1,X0),X0)
| subset(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c14,c57]) ).
cnf(p120,plain,
( ~ member(sk1(X0,X1),X1)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[p118,c57]) ).
cnf(p1734,plain,
( subset(sk14,domain_of(sk15))
| subset(sk14,domain_of(sk15)) ),
inference(resolution,[status(thm)],[p1729,p120]) ).
cnf(p1738,plain,
subset(sk14,domain_of(sk15)),
inference(factoring,[status(thm)],[p1734]) ).
cnf(p2087,plain,
~ subset(sk14,range(sk12,sk13,sk15)),
inference(resolution,[status(thm)],[p2079,p1738]) ).
cnf(p2638,plain,
~ subset(sk14,range_of(sk15)),
inference(demodulation,[status(thm)],[p2637,p2087]) ).
cnf(c1,plain,
( member(X1,range_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)],[f0_sk]) ).
cnf(p68,plain,
( member(X0,range_of(X1))
| ~ member(ordered_pair(X2,X0),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[status(thm)],[c1,c57]) ).
cnf(p300,plain,
( member(X2,range_of(X0))
| ~ member(ordered_pair(X1,X2),X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(resolution,[status(thm)],[p68,c57]) ).
cnf(p419,plain,
( member(X1,range_of(sk15))
| ~ member(ordered_pair(X0,X1),sk15) ),
inference(resolution,[status(thm)],[p300,p133]) ).
cnf(p1730,plain,
( member(sk1(sk14,X0),range_of(sk15))
| subset(sk14,X0) ),
inference(resolution,[status(thm)],[p971,p419]) ).
cnf(p1741,plain,
( subset(sk14,range_of(sk15))
| subset(sk14,range_of(sk15)) ),
inference(resolution,[status(thm)],[p1730,p120]) ).
cnf(p1745,plain,
subset(sk14,range_of(sk15)),
inference(factoring,[status(thm)],[p1741]) ).
cnf(p2651,plain,
$false,
inference(resolution,[status(thm)],[p2638,p1745]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET667+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.38 % Computer : n018.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Thu Sep 24 11:38:49 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 29.34/4.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.34/4.76 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------