%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET678+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 : Sun Sep 27 08:36:48 AM UTC 2026
% Result : Theorem 17.74s 2.69s
% Output : CNFRefutation 17.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 17
% Syntax : Number of formulae : 102 ( 25 unt; 0 def)
% Number of atoms : 314 ( 32 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 354 ( 142 ~; 142 |; 19 &)
% ( 6 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-3 aty)
% Number of variables : 181 ( 7 sgn 57 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(domain_of(C),B)
=> compose(identity_relation_of(B),C) = C ) ) ),
file('theBenchmark.p',p1) ).
fof(p2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(range_of(C),B)
=> compose(C,identity_relation_of(B)) = C ) ) ),
file('theBenchmark.p',p2) ).
fof(p7,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('theBenchmark.p',p7) ).
fof(p13,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) ) ),
file('theBenchmark.p',p13) ).
fof(p15,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('theBenchmark.p',p15) ).
fof(p19,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('theBenchmark.p',p19) ).
fof(p22,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('theBenchmark.p',p22) ).
fof(p25,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('theBenchmark.p',p25) ).
fof(p26,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('theBenchmark.p',p26) ).
fof(p27,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('theBenchmark.p',p27) ).
fof(p28,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('theBenchmark.p',p28) ).
fof(p32,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('theBenchmark.p',p32) ).
fof(p33,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('theBenchmark.p',p33) ).
fof(p34,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('theBenchmark.p',p34) ).
fof(p35,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(range(B,C,D),subset_type(C)) ) ) ),
file('theBenchmark.p',p35) ).
fof(p38,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p38) ).
fof(prove_relset_1_45,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,identity_relation_of_type(B))
=> ( compose(identity_relation_of(B),C) = C
& compose(C,identity_relation_of(B)) = C ) ) ),
file('theBenchmark.p',prove_relset_1_45) ).
fof(prove_relset_1_45_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,identity_relation_of_type(B))
=> ( compose(identity_relation_of(B),C) = C
& compose(C,identity_relation_of(B)) = C ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_45]) ).
cnf(c_40,plain,
( ~ relation_like(A)
| ilf_type(A,binary_relation_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p13]) ).
cnf(c_48,plain,
( relation_like(C)
| ~ ilf_type(C,subset_type(cross_product(A,B)))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p25]) ).
cnf(c_54,plain,
( ilf_type(C,binary_relation_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(cross_product(A,B)))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_48,c_40]) ).
fof(nnf_39,plain,
? [B] :
( ? [C] :
( ( compose(identity_relation_of(B),C) != C
| compose(C,identity_relation_of(B)) != C )
& ilf_type(C,identity_relation_of_type(B)) )
& ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[prove_relset_1_45_neg]) ).
fof(sk_prove_relset_1_45_neg,plain,
( ( compose(identity_relation_of(sK1),sK0) != sK0
| compose(sK0,identity_relation_of(sK1)) != sK0 )
& ilf_type(sK0,identity_relation_of_type(sK1))
& ilf_type(sK1,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(B,sK1),skolemize(C,sK0)],[nnf_39]) ).
cnf(c_66,negated_conjecture,
( compose(identity_relation_of(sK1),sK0) != sK0
| compose(sK0,identity_relation_of(sK1)) != sK0 ),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_45_neg]) ).
cnf(c_67,negated_conjecture,
ilf_type(sK0,identity_relation_of_type(sK1)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_45_neg]) ).
cnf(c_69,plain,
ilf_type(A,set_type),
inference(clausify,[status(thm)],[p38]) ).
cnf(c_74,plain,
( ilf_type(range(A,B,C),subset_type(B))
| ~ ilf_type(C,relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p35]) ).
cnf(c_15952,plain,
( ilf_type(range(C,A,B),subset_type(A))
| ~ ilf_type(B,relation_type(C,A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_69,c_74]) ).
cnf(c_75,plain,
( ilf_type(range(B,C,A),subset_type(C))
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_69,c_15952]) ).
cnf(c_76,plain,
( range(A,B,C) = range_of(C)
| ~ ilf_type(C,relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p34]) ).
cnf(c_15953,plain,
( range(C,A,B) = range_of(B)
| ~ ilf_type(B,relation_type(C,A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_69,c_76]) ).
cnf(c_77,plain,
( range(B,C,A) = range_of(A)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_69,c_15953]) ).
cnf(c_78,plain,
( ilf_type(domain(A,B,C),subset_type(A))
| ~ ilf_type(C,relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p33]) ).
cnf(c_15954,plain,
( ilf_type(domain(C,A,B),subset_type(C))
| ~ ilf_type(B,relation_type(C,A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_69,c_78]) ).
cnf(c_79,plain,
( ilf_type(domain(B,C,A),subset_type(B))
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_69,c_15954]) ).
cnf(c_80,plain,
( domain(A,B,C) = domain_of(C)
| ~ ilf_type(C,relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p32]) ).
cnf(c_15955,plain,
( domain(C,A,B) = domain_of(B)
| ~ ilf_type(B,relation_type(C,A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_69,c_80]) ).
cnf(c_81,plain,
( domain(B,C,A) = domain_of(A)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_69,c_15955]) ).
cnf(c_91,plain,
( member(A,B)
| ~ ilf_type(A,member_type(B))
| ~ ilf_type(B,set_type)
| empty(B)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p28]) ).
cnf(c_15956,plain,
( member(B,A)
| ~ ilf_type(B,member_type(A))
| ~ ilf_type(A,set_type)
| empty(A) ),
inference(resolve,[status(thm)],[c_69,c_91]) ).
cnf(c_92,plain,
( member(B,A)
| ~ ilf_type(B,member_type(A))
| empty(A) ),
inference(resolve,[status(thm)],[c_69,c_15956]) ).
cnf(c_94,plain,
( ~ empty(power_set(A))
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p27]) ).
cnf(c_95,plain,
~ empty(power_set(A)),
inference(resolve,[status(thm)],[c_69,c_94]) ).
cnf(c_101,plain,
( member(C,B)
| ~ member(C,A)
| ~ ilf_type(C,set_type)
| ~ member(A,power_set(B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p26]) ).
cnf(c_15957,plain,
( member(C,A)
| ~ member(C,B)
| ~ ilf_type(C,set_type)
| ~ member(B,power_set(A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_69,c_101]) ).
cnf(c_15958,plain,
( member(C,B)
| ~ member(C,A)
| ~ ilf_type(C,set_type)
| ~ member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_69,c_15957]) ).
cnf(c_102,plain,
( member(C,B)
| ~ member(C,A)
| ~ member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_69,c_15958]) ).
cnf(c_107,plain,
( ilf_type(B,member_type(power_set(A)))
| ~ ilf_type(B,subset_type(A))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p22]) ).
cnf(c_15959,plain,
( ilf_type(A,member_type(power_set(B)))
| ~ ilf_type(A,subset_type(B))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_69,c_107]) ).
cnf(c_108,plain,
( ilf_type(A,member_type(power_set(B)))
| ~ ilf_type(A,subset_type(B)) ),
inference(resolve,[status(thm)],[c_69,c_15959]) ).
fof(nnf_19,plain,
! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) )
| subset(B,C) )
& ( ! [X0] :
( member(X0,C)
| ~ member(X0,B)
| ~ ilf_type(X0,set_type) )
| ~ subset(B,C) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p19]) ).
fof(sk_p19_sk,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK2(B,C),C)
& member(sK2(B,C),B)
& ilf_type(sK2(B,C),set_type) )
| subset(B,C) )
& ( ! [X0] :
( member(X0,C)
| ~ member(X0,B)
| ~ ilf_type(X0,set_type) )
| ~ subset(B,C) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(D,sK2(B,C))],[nnf_19]) ).
fof(sk_p19,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK2(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1)
| ~ ilf_type(VAR_1,set_type)
| ~ ilf_type(VAR_0,set_type) )
& ! [VAR_0,VAR_1] :
( member(sK2(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1)
| ~ ilf_type(VAR_1,set_type)
| ~ ilf_type(VAR_0,set_type) )
& ! [VAR_0,VAR_1] :
( ilf_type(sK2(VAR_0,VAR_1),set_type)
| subset(VAR_0,VAR_1)
| ~ ilf_type(VAR_1,set_type)
| ~ ilf_type(VAR_0,set_type) )
& ! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ ilf_type(VAR_2,set_type)
| ~ subset(VAR_0,VAR_1)
| ~ ilf_type(VAR_1,set_type)
| ~ ilf_type(VAR_0,set_type) ) ),
inference(cnf_transformation,[status(thm)],[sk_p19_sk]) ).
cnf(c_112,plain,
( ~ member(sK2(A,B),B)
| subset(A,B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_p19]) ).
cnf(c_15960,plain,
( ~ member(sK2(B,A),A)
| subset(B,A)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_69,c_112]) ).
cnf(c_113,plain,
( ~ member(sK2(A,B),B)
| subset(A,B) ),
inference(resolve,[status(thm)],[c_69,c_15960]) ).
cnf(c_114,plain,
( member(sK2(A,B),A)
| subset(A,B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_p19]) ).
cnf(c_15961,plain,
( member(sK2(B,A),B)
| subset(B,A)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_69,c_114]) ).
cnf(c_115,plain,
( member(sK2(A,B),A)
| subset(A,B) ),
inference(resolve,[status(thm)],[c_69,c_15961]) ).
cnf(c_121,plain,
( ilf_type(C,subset_type(cross_product(A,B)))
| ~ ilf_type(C,relation_type(A,B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p15]) ).
cnf(c_15962,plain,
( ilf_type(B,subset_type(cross_product(C,A)))
| ~ ilf_type(B,relation_type(C,A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_69,c_121]) ).
cnf(c_122,plain,
( ilf_type(A,subset_type(cross_product(B,C)))
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_69,c_15962]) ).
cnf(c_137,plain,
( ilf_type(B,relation_type(A,A))
| ~ ilf_type(B,identity_relation_of_type(A))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p7]) ).
cnf(c_15963,plain,
( ilf_type(A,relation_type(B,B))
| ~ ilf_type(A,identity_relation_of_type(B))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_69,c_137]) ).
cnf(c_138,plain,
( ilf_type(A,relation_type(B,B))
| ~ ilf_type(A,identity_relation_of_type(B)) ),
inference(resolve,[status(thm)],[c_69,c_15963]) ).
cnf(c_155,plain,
( compose(B,identity_relation_of(A)) = B
| ~ subset(range_of(B),A)
| ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p2]) ).
cnf(c_156,plain,
( compose(A,identity_relation_of(B)) = A
| ~ subset(range_of(A),B)
| ~ ilf_type(A,binary_relation_type) ),
inference(resolve,[status(thm)],[c_69,c_155]) ).
cnf(c_157,plain,
( compose(identity_relation_of(A),B) = B
| ~ subset(domain_of(B),A)
| ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p1]) ).
cnf(c_158,plain,
( compose(identity_relation_of(B),A) = A
| ~ subset(domain_of(A),B)
| ~ ilf_type(A,binary_relation_type) ),
inference(resolve,[status(thm)],[c_69,c_157]) ).
cnf(c_15964,plain,
( ilf_type(B,binary_relation_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(B,subset_type(cross_product(C,A)))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_69,c_54]) ).
cnf(c_15965,plain,
( ilf_type(A,binary_relation_type)
| ~ ilf_type(A,set_type)
| ~ ilf_type(A,subset_type(cross_product(B,C))) ),
inference(resolve,[status(thm)],[c_69,c_15964]) ).
cnf(c_185,plain,
( ilf_type(A,binary_relation_type)
| ~ ilf_type(A,subset_type(cross_product(B,C))) ),
inference(resolve,[status(thm)],[c_69,c_15965]) ).
cnf(c_216,plain,
( member(sK2(A,B),C)
| ~ member(A,power_set(C))
| subset(A,B) ),
inference(resolve,[status(thm)],[c_115,c_102]) ).
cnf(c_243,plain,
ilf_type(sK0,relation_type(sK1,sK1)),
inference(resolve,[status(thm)],[c_138,c_67]) ).
cnf(c_344,plain,
ilf_type(sK0,subset_type(cross_product(sK1,sK1))),
inference(resolve,[status(thm)],[c_243,c_122]) ).
cnf(c_345,plain,
domain(sK1,sK1,sK0) = domain_of(sK0),
inference(resolve,[status(thm)],[c_243,c_81]) ).
cnf(c_15966,plain,
ilf_type(domain(sK1,sK1,sK0),subset_type(sK1)),
inference(resolve,[status(thm)],[c_243,c_79]) ).
cnf(c_346,plain,
ilf_type(domain_of(sK0),subset_type(sK1)),
inference(paramod,[status(thm)],[c_345,c_15966]) ).
cnf(c_347,plain,
range(sK1,sK1,sK0) = range_of(sK0),
inference(resolve,[status(thm)],[c_243,c_77]) ).
cnf(c_15967,plain,
ilf_type(range(sK1,sK1,sK0),subset_type(sK1)),
inference(resolve,[status(thm)],[c_243,c_75]) ).
cnf(c_348,plain,
ilf_type(range_of(sK0),subset_type(sK1)),
inference(paramod,[status(thm)],[c_347,c_15967]) ).
cnf(c_362,plain,
ilf_type(domain_of(sK0),member_type(power_set(sK1))),
inference(resolve,[status(thm)],[c_346,c_108]) ).
cnf(c_380,plain,
ilf_type(range_of(sK0),member_type(power_set(sK1))),
inference(resolve,[status(thm)],[c_348,c_108]) ).
cnf(c_643,plain,
ilf_type(sK0,binary_relation_type),
inference(resolve,[status(thm)],[c_344,c_185]) ).
cnf(c_653,plain,
( compose(identity_relation_of(A),sK0) = sK0
| ~ subset(domain_of(sK0),A) ),
inference(resolve,[status(thm)],[c_643,c_158]) ).
cnf(c_654,plain,
( compose(sK0,identity_relation_of(A)) = sK0
| ~ subset(range_of(sK0),A) ),
inference(resolve,[status(thm)],[c_643,c_156]) ).
cnf(c_15968,plain,
( member(domain_of(sK0),power_set(sK1))
| empty(power_set(sK1)) ),
inference(resolve,[status(thm)],[c_362,c_92]) ).
cnf(c_716,plain,
member(domain_of(sK0),power_set(sK1)),
inference(resolve,[status(thm)],[c_95,c_15968]) ).
cnf(c_717,plain,
( member(sK2(domain_of(sK0),A),sK1)
| subset(domain_of(sK0),A) ),
inference(resolve,[status(thm)],[c_716,c_216]) ).
cnf(c_15969,plain,
( member(range_of(sK0),power_set(sK1))
| empty(power_set(sK1)) ),
inference(resolve,[status(thm)],[c_380,c_92]) ).
cnf(c_783,plain,
member(range_of(sK0),power_set(sK1)),
inference(resolve,[status(thm)],[c_95,c_15969]) ).
cnf(c_795,plain,
( member(A,sK1)
| ~ member(A,range_of(sK0)) ),
inference(resolve,[status(thm)],[c_783,c_102]) ).
cnf(c_15970,plain,
( subset(domain_of(sK0),sK1)
| subset(domain_of(sK0),sK1) ),
inference(resolve,[status(thm)],[c_717,c_113]) ).
cnf(c_15842,plain,
subset(domain_of(sK0),sK1),
inference(copy,[status(thm)],[c_15970]) ).
cnf(c_15845,plain,
compose(identity_relation_of(sK1),sK0) = sK0,
inference(resolve,[status(thm)],[c_15842,c_653]) ).
cnf(c_15971,negated_conjecture,
( sK0 != sK0
| compose(sK0,identity_relation_of(sK1)) != sK0 ),
inference(paramod,[status(thm)],[c_15845,c_66]) ).
cnf(c_15846,negated_conjecture,
compose(sK0,identity_relation_of(sK1)) != sK0,
inference(copy,[status(thm)],[c_15971]) ).
cnf(c_15847,negated_conjecture,
~ subset(range_of(sK0),sK1),
inference(resolve,[status(thm)],[c_654,c_15846]) ).
cnf(c_15866,plain,
member(sK2(range_of(sK0),sK1),range_of(sK0)),
inference(resolve,[status(thm)],[c_15847,c_115]) ).
cnf(c_15869,plain,
~ member(sK2(range_of(sK0),sK1),sK1),
inference(resolve,[status(thm)],[c_113,c_15847]) ).
cnf(c_15972,plain,
~ member(sK2(range_of(sK0),sK1),range_of(sK0)),
inference(resolve,[status(thm)],[c_795,c_15869]) ).
cnf(c_15951,plain,
$false,
inference(resolve,[status(thm)],[c_15866,c_15972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET678+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sat Sep 26 08:05:04 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.30 % Process 88657 was started by sandbox2 on n012,
% 0.03/0.30 % Sat Sep 26 08:05:04 2026
% 0.03/0.30 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.30
% 0.03/0.30 % From the command line: assign(max_seconds, 300).
% 17.74/2.69
% 17.74/2.69 % given #500 (T,wt=14): 3601 ilf_type(f13(c2),member_type(c2)) | ilf_type(range_of(c3),subset_type(A)). [resolve(3446,a,1179,b)].
% 17.74/2.69
% 17.74/2.69 % SZS status Theorem for theBenchmark
% 17.74/2.69
% 17.74/2.69 % Proof 1 at 1.93 (+ 0.38) seconds.
% 17.74/2.69 % Length of proof is 75.
% 17.74/2.69 % Level of proof is 14.
% 17.74/2.69 % Maximum clause weight is 24.000.
% 17.74/2.69 % Given clauses 994.
% 17.74/2.69
% 17.74/2.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------