%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET657+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 : n008.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 08:36:45 AM UTC 2026
% Result : Theorem 0.09s 0.48s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 17
% Syntax : Number of formulae : 112 ( 32 unt; 0 def)
% Number of atoms : 339 ( 17 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 386 ( 159 ~; 157 |; 19 &)
% ( 6 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-3 aty)
% Number of variables : 209 ( 12 sgn 59 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p3,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ) ) ) ),
file('theBenchmark.p',p3) ).
fof(p5,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> field_of(B) = union(domain_of(B),range_of(B)) ),
file('theBenchmark.p',p5) ).
fof(p7,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',p7) ).
fof(p9,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',p9) ).
fof(p10,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> union(B,C) = union(C,B) ) ),
file('theBenchmark.p',p10) ).
fof(p14,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) ) ),
file('theBenchmark.p',p14) ).
fof(p16,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',p16) ).
fof(p21,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',p21) ).
fof(p22,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('theBenchmark.p',p22) ).
fof(p23,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',p23) ).
fof(p27,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',p27) ).
fof(p33,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',p33) ).
fof(p34,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',p34) ).
fof(p35,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',p35) ).
fof(p36,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',p36) ).
fof(p37,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p37) ).
fof(prove_relset_1_19,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> subset(field_of(D),union(B,C)) ) ) ),
file('theBenchmark.p',prove_relset_1_19) ).
fof(prove_relset_1_19_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> subset(field_of(D),union(B,C)) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_19]) ).
cnf(c_39,plain,
( ~ relation_like(A)
| ilf_type(A,binary_relation_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p14]) ).
cnf(c_47,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)],[p27]) ).
cnf(c_53,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_47,c_39]) ).
fof(nnf_38,plain,
? [B] :
( ? [C] :
( ? [D] :
( ~ subset(field_of(D),union(B,C))
& ilf_type(D,relation_type(B,C)) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[prove_relset_1_19_neg]) ).
fof(sk_prove_relset_1_19_neg,plain,
( ~ subset(field_of(sK0),union(sK1,sK2))
& ilf_type(sK0,relation_type(sK1,sK2))
& ilf_type(sK2,set_type)
& ilf_type(sK1,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK0]),skolemize(B,sK1),skolemize(C,sK2),skolemize(D,sK0)],[nnf_38]) ).
cnf(c_65,negated_conjecture,
~ subset(field_of(sK0),union(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_19_neg]) ).
cnf(c_66,negated_conjecture,
ilf_type(sK0,relation_type(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_19_neg]) ).
cnf(c_69,plain,
ilf_type(A,set_type),
inference(clausify,[status(thm)],[p37]) ).
cnf(c_70,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)],[p36]) ).
cnf(c_663,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_70]) ).
cnf(c_71,plain,
( ilf_type(range(B,C,A),subset_type(C))
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_69,c_663]) ).
cnf(c_72,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)],[p35]) ).
cnf(c_664,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_72]) ).
cnf(c_73,plain,
( range(B,C,A) = range_of(A)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_69,c_664]) ).
cnf(c_74,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)],[p34]) ).
cnf(c_665,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_74]) ).
cnf(c_75,plain,
( ilf_type(domain(B,C,A),subset_type(B))
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_69,c_665]) ).
cnf(c_76,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)],[p33]) ).
cnf(c_666,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_76]) ).
cnf(c_77,plain,
( domain(B,C,A) = domain_of(A)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_69,c_666]) ).
cnf(c_101,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)],[p23]) ).
cnf(c_667,plain,
( member(B,A)
| ~ ilf_type(B,member_type(A))
| ~ ilf_type(A,set_type)
| empty(A) ),
inference(resolve,[status(thm)],[c_69,c_101]) ).
cnf(c_102,plain,
( member(B,A)
| ~ ilf_type(B,member_type(A))
| empty(A) ),
inference(resolve,[status(thm)],[c_69,c_667]) ).
cnf(c_104,plain,
( ~ empty(power_set(A))
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p22]) ).
cnf(c_105,plain,
~ empty(power_set(A)),
inference(resolve,[status(thm)],[c_69,c_104]) ).
cnf(c_111,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)],[p21]) ).
cnf(c_668,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_111]) ).
cnf(c_669,plain,
( member(C,B)
| ~ member(C,A)
| ~ ilf_type(C,set_type)
| ~ member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_69,c_668]) ).
cnf(c_112,plain,
( member(C,B)
| ~ member(C,A)
| ~ member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_69,c_669]) ).
cnf(c_119,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)],[p16]) ).
cnf(c_670,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_119]) ).
cnf(c_120,plain,
( ilf_type(A,member_type(power_set(B)))
| ~ ilf_type(A,subset_type(B)) ),
inference(resolve,[status(thm)],[c_69,c_670]) ).
cnf(c_123,plain,
( union(B,A) = union(A,B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p10]) ).
cnf(c_671,plain,
( union(A,B) = union(B,A)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_69,c_123]) ).
cnf(c_124,plain,
union(A,B) = union(B,A),
inference(resolve,[status(thm)],[c_69,c_671]) ).
fof(nnf_9,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)],[p9]) ).
fof(sk_p9_sk,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK3(B,C),C)
& member(sK3(B,C),B)
& ilf_type(sK3(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,[sK3]),skolemize(D,sK3(B,C))],[nnf_9]) ).
fof(sk_p9,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK3(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(sK3(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(sK3(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_p9_sk]) ).
cnf(c_125,plain,
( ~ member(sK3(A,B),B)
| subset(A,B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_p9]) ).
cnf(c_672,plain,
( ~ member(sK3(B,A),A)
| subset(B,A)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_69,c_125]) ).
cnf(c_126,plain,
( ~ member(sK3(A,B),B)
| subset(A,B) ),
inference(resolve,[status(thm)],[c_69,c_672]) ).
cnf(c_127,plain,
( member(sK3(A,B),A)
| subset(A,B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_p9]) ).
cnf(c_673,plain,
( member(sK3(B,A),B)
| subset(B,A)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_69,c_127]) ).
cnf(c_128,plain,
( member(sK3(A,B),A)
| subset(A,B) ),
inference(resolve,[status(thm)],[c_69,c_673]) ).
cnf(c_134,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)],[p7]) ).
cnf(c_674,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_134]) ).
cnf(c_135,plain,
( ilf_type(A,subset_type(cross_product(B,C)))
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_69,c_674]) ).
cnf(c_138,plain,
( field_of(A) = union(domain_of(A),range_of(A))
| ~ ilf_type(A,binary_relation_type) ),
inference(clausify,[status(thm)],[p5]) ).
cnf(c_140,plain,
( ~ member(C,B)
| member(C,union(A,B))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p3]) ).
cnf(c_675,plain,
( ~ member(B,A)
| member(B,union(C,A))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_69,c_140]) ).
cnf(c_676,plain,
( ~ member(A,C)
| member(A,union(B,C))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_69,c_675]) ).
cnf(c_141,plain,
( ~ member(A,C)
| member(A,union(B,C)) ),
inference(resolve,[status(thm)],[c_69,c_676]) ).
cnf(c_142,plain,
( ~ member(C,A)
| member(C,union(A,B))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p3]) ).
cnf(c_677,plain,
( ~ member(B,C)
| member(B,union(C,A))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_69,c_142]) ).
cnf(c_678,plain,
( ~ member(A,B)
| member(A,union(B,C))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_69,c_677]) ).
cnf(c_143,plain,
( ~ member(A,B)
| member(A,union(B,C)) ),
inference(resolve,[status(thm)],[c_69,c_678]) ).
cnf(c_144,plain,
( member(C,B)
| member(C,A)
| ~ member(C,union(A,B))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p3]) ).
cnf(c_679,plain,
( member(B,A)
| member(B,C)
| ~ member(B,union(C,A))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_69,c_144]) ).
cnf(c_680,plain,
( member(A,C)
| member(A,B)
| ~ member(A,union(B,C))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_69,c_679]) ).
cnf(c_145,plain,
( member(A,C)
| member(A,B)
| ~ member(A,union(B,C)) ),
inference(resolve,[status(thm)],[c_69,c_680]) ).
cnf(c_681,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_53]) ).
cnf(c_682,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_681]) ).
cnf(c_174,plain,
( ilf_type(A,binary_relation_type)
| ~ ilf_type(A,subset_type(cross_product(B,C))) ),
inference(resolve,[status(thm)],[c_69,c_682]) ).
cnf(c_181,plain,
ilf_type(range(sK1,sK2,sK0),subset_type(sK2)),
inference(resolve,[status(thm)],[c_71,c_66]) ).
cnf(c_182,plain,
range(sK1,sK2,sK0) = range_of(sK0),
inference(resolve,[status(thm)],[c_73,c_66]) ).
cnf(c_183,plain,
ilf_type(range_of(sK0),subset_type(sK2)),
inference(paramod,[status(thm)],[c_182,c_181]) ).
cnf(c_184,plain,
ilf_type(domain(sK1,sK2,sK0),subset_type(sK1)),
inference(resolve,[status(thm)],[c_75,c_66]) ).
cnf(c_185,plain,
domain(sK1,sK2,sK0) = domain_of(sK0),
inference(resolve,[status(thm)],[c_77,c_66]) ).
cnf(c_186,plain,
ilf_type(domain_of(sK0),subset_type(sK1)),
inference(paramod,[status(thm)],[c_185,c_184]) ).
cnf(c_225,negated_conjecture,
~ member(sK3(field_of(sK0),union(sK1,sK2)),union(sK1,sK2)),
inference(resolve,[status(thm)],[c_126,c_65]) ).
cnf(c_226,plain,
member(sK3(field_of(sK0),union(sK1,sK2)),field_of(sK0)),
inference(resolve,[status(thm)],[c_128,c_65]) ).
cnf(c_237,plain,
ilf_type(sK0,subset_type(cross_product(sK1,sK2))),
inference(resolve,[status(thm)],[c_135,c_66]) ).
cnf(c_304,plain,
~ member(sK3(field_of(sK0),union(sK1,sK2)),sK1),
inference(resolve,[status(thm)],[c_143,c_225]) ).
cnf(c_305,plain,
~ member(sK3(field_of(sK0),union(sK1,sK2)),sK2),
inference(resolve,[status(thm)],[c_141,c_225]) ).
cnf(c_335,plain,
ilf_type(range_of(sK0),member_type(power_set(sK2))),
inference(resolve,[status(thm)],[c_183,c_120]) ).
cnf(c_336,plain,
ilf_type(domain_of(sK0),member_type(power_set(sK1))),
inference(resolve,[status(thm)],[c_186,c_120]) ).
cnf(c_401,plain,
ilf_type(sK0,binary_relation_type),
inference(resolve,[status(thm)],[c_237,c_174]) ).
cnf(c_439,plain,
field_of(sK0) = union(domain_of(sK0),range_of(sK0)),
inference(resolve,[status(thm)],[c_401,c_138]) ).
cnf(c_529,plain,
~ member(sK3(union(domain_of(sK0),range_of(sK0)),union(sK1,sK2)),sK2),
inference(paramod,[status(thm)],[c_439,c_305]) ).
cnf(c_530,plain,
~ member(sK3(union(domain_of(sK0),range_of(sK0)),union(sK1,sK2)),sK1),
inference(paramod,[status(thm)],[c_439,c_304]) ).
cnf(c_683,plain,
member(sK3(union(domain_of(sK0),range_of(sK0)),union(sK1,sK2)),field_of(sK0)),
inference(paramod,[status(thm)],[c_439,c_226]) ).
cnf(c_532,plain,
member(sK3(union(domain_of(sK0),range_of(sK0)),union(sK1,sK2)),union(domain_of(sK0),range_of(sK0))),
inference(paramod,[status(thm)],[c_439,c_683]) ).
cnf(c_684,plain,
( member(range_of(sK0),power_set(sK2))
| empty(power_set(sK2)) ),
inference(resolve,[status(thm)],[c_335,c_102]) ).
cnf(c_566,plain,
member(range_of(sK0),power_set(sK2)),
inference(resolve,[status(thm)],[c_105,c_684]) ).
cnf(c_685,plain,
( member(A,sK2)
| ~ member(A,range_of(sK0)) ),
inference(resolve,[status(thm)],[c_112,c_566]) ).
cnf(c_576,plain,
~ member(sK3(union(domain_of(sK0),range_of(sK0)),union(sK1,sK2)),range_of(sK0)),
inference(resolve,[status(thm)],[c_685,c_529]) ).
cnf(c_686,plain,
( member(domain_of(sK0),power_set(sK1))
| empty(power_set(sK1)) ),
inference(resolve,[status(thm)],[c_336,c_102]) ).
cnf(c_577,plain,
member(domain_of(sK0),power_set(sK1)),
inference(resolve,[status(thm)],[c_105,c_686]) ).
cnf(c_687,plain,
( member(A,sK1)
| ~ member(A,domain_of(sK0)) ),
inference(resolve,[status(thm)],[c_112,c_577]) ).
cnf(c_592,plain,
~ member(sK3(union(domain_of(sK0),range_of(sK0)),union(sK1,sK2)),domain_of(sK0)),
inference(resolve,[status(thm)],[c_687,c_530]) ).
cnf(c_688,plain,
( member(sK3(union(domain_of(sK0),range_of(sK0)),union(sK1,sK2)),A)
| ~ member(sK3(union(domain_of(sK0),range_of(sK0)),union(sK1,sK2)),union(range_of(sK0),A)) ),
inference(resolve,[status(thm)],[c_145,c_576]) ).
cnf(c_689,plain,
~ member(sK3(union(domain_of(sK0),range_of(sK0)),union(sK1,sK2)),union(range_of(sK0),domain_of(sK0))),
inference(resolve,[status(thm)],[c_688,c_592]) ).
cnf(c_690,plain,
~ member(sK3(union(domain_of(sK0),range_of(sK0)),union(sK1,sK2)),union(domain_of(sK0),range_of(sK0))),
inference(paramod,[status(thm)],[c_124,c_689]) ).
cnf(c_662,plain,
$false,
inference(resolve,[status(thm)],[c_532,c_690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET657+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n008.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 : Sat Sep 26 08:04:09 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 3158490 was started by sandbox2 on n008,
% 0.09/0.38 % Sat Sep 26 08:04:09 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 0.09/0.48
% 0.09/0.48 % SZS status Theorem for theBenchmark
% 0.09/0.48
% 0.09/0.48 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.09/0.48 % Length of proof is 78.
% 0.09/0.48 % Level of proof is 8.
% 0.09/0.48 % Maximum clause weight is 18.000.
% 0.09/0.48 % Given clauses 117.
% 0.09/0.48
% 0.09/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------