%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET659+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 : n003.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 8.97s 1.65s
% Output : CNFRefutation 8.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 14
% Syntax : Number of formulae : 103 ( 17 unt; 0 def)
% Number of atoms : 395 ( 60 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 463 ( 171 ~; 200 |; 41 &)
% ( 8 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 189 ( 12 sgn 69 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,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('theBenchmark.p',p1) ).
fof(p3,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('theBenchmark.p',p3) ).
fof(p4,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
<=> member(D,C) ) )
=> B = C ) ) ),
file('theBenchmark.p',p4) ).
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(p15,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( ilf_type(B,set_type)
& relation_like(B) ) ) ),
file('theBenchmark.p',p15) ).
fof(p17,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',p17) ).
fof(p22,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',p22) ).
fof(p23,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('theBenchmark.p',p23) ).
fof(p24,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',p24) ).
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(p30,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',p30) ).
fof(p31,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',p31) ).
fof(p34,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p34) ).
fof(prove_relset_1_22,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('theBenchmark.p',prove_relset_1_22) ).
fof(prove_relset_1_22_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(assume_negation,[status(cth)],[prove_relset_1_22]) ).
cnf(c_36,plain,
( ~ relation_like(A)
| ilf_type(A,binary_relation_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p15]) ).
cnf(c_44,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_50,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_44,c_36]) ).
fof(nnf_35,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
| ! [X0] :
( ? [X1] :
( member(ordered_pair(X0,X1),D)
& ilf_type(X1,set_type) )
| ~ member(X0,C)
| ~ ilf_type(X0,set_type) ) )
& ilf_type(D,relation_type(C,B)) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[prove_relset_1_22_neg]) ).
fof(sk_prove_relset_1_22_neg_sk,plain,
( ( domain(sK2,sK3,sK1) != sK2
| ( ! [F] :
( ~ member(ordered_pair(sK0,F),sK1)
| ~ ilf_type(F,set_type) )
& member(sK0,sK2)
& ilf_type(sK0,set_type) ) )
& ( domain(sK2,sK3,sK1) = sK2
| ! [X0] :
( ( member(ordered_pair(X0,sK4(X0)),sK1)
& ilf_type(sK4(X0),set_type) )
| ~ member(X0,sK2)
| ~ ilf_type(X0,set_type) ) )
& ilf_type(sK1,relation_type(sK2,sK3))
& ilf_type(sK2,set_type)
& ilf_type(sK3,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK2,sK1,sK4,sK0]),skolemize(B,sK3),skolemize(C,sK2),skolemize(D,sK1),skolemize(X1,sK4(X0)),skolemize(E,sK0)],[nnf_35]) ).
fof(sk_prove_relset_1_22_neg,plain,
( ! [VAR_0] :
( domain(sK2,sK3,sK1) != sK2
| ~ member(ordered_pair(sK0,VAR_0),sK1)
| ~ ilf_type(VAR_0,set_type) )
& ( domain(sK2,sK3,sK1) != sK2
| member(sK0,sK2) )
& ( domain(sK2,sK3,sK1) != sK2
| ilf_type(sK0,set_type) )
& ! [VAR_0] :
( domain(sK2,sK3,sK1) = sK2
| member(ordered_pair(VAR_0,sK4(VAR_0)),sK1)
| ~ member(VAR_0,sK2)
| ~ ilf_type(VAR_0,set_type) )
& ! [VAR_0] :
( domain(sK2,sK3,sK1) = sK2
| ilf_type(sK4(VAR_0),set_type)
| ~ member(VAR_0,sK2)
| ~ ilf_type(VAR_0,set_type) )
& ilf_type(sK1,relation_type(sK2,sK3))
& ilf_type(sK2,set_type)
& ilf_type(sK3,set_type) ),
inference(cnf_transformation,[status(thm)],[sk_prove_relset_1_22_neg_sk]) ).
cnf(c_62,negated_conjecture,
( domain(sK2,sK3,sK1) != sK2
| ~ member(ordered_pair(sK0,A),sK1)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_22_neg]) ).
cnf(c_63,negated_conjecture,
( domain(sK2,sK3,sK1) != sK2
| member(sK0,sK2) ),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_22_neg]) ).
cnf(c_65,negated_conjecture,
( domain(sK2,sK3,sK1) = sK2
| member(ordered_pair(A,sK4(A)),sK1)
| ~ member(A,sK2)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_22_neg]) ).
cnf(c_67,negated_conjecture,
ilf_type(sK1,relation_type(sK2,sK3)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_22_neg]) ).
cnf(c_70,plain,
ilf_type(A,set_type),
inference(clausify,[status(thm)],[p34]) ).
cnf(c_75,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)],[p31]) ).
cnf(c_6052,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_70,c_75]) ).
cnf(c_76,plain,
( ilf_type(domain(B,C,A),subset_type(B))
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_70,c_6052]) ).
cnf(c_77,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)],[p30]) ).
cnf(c_6053,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_70,c_77]) ).
cnf(c_78,plain,
( domain(B,C,A) = domain_of(A)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_70,c_6053]) ).
cnf(c_88,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)],[p24]) ).
cnf(c_6054,plain,
( member(B,A)
| ~ ilf_type(B,member_type(A))
| ~ ilf_type(A,set_type)
| empty(A) ),
inference(resolve,[status(thm)],[c_70,c_88]) ).
cnf(c_89,plain,
( member(B,A)
| ~ ilf_type(B,member_type(A))
| empty(A) ),
inference(resolve,[status(thm)],[c_70,c_6054]) ).
cnf(c_91,plain,
( ~ empty(power_set(A))
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p23]) ).
cnf(c_92,plain,
~ empty(power_set(A)),
inference(resolve,[status(thm)],[c_70,c_91]) ).
cnf(c_98,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)],[p22]) ).
cnf(c_6055,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_70,c_98]) ).
cnf(c_6056,plain,
( member(C,B)
| ~ member(C,A)
| ~ ilf_type(C,set_type)
| ~ member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_70,c_6055]) ).
cnf(c_99,plain,
( member(C,B)
| ~ member(C,A)
| ~ member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_70,c_6056]) ).
cnf(c_122,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)],[p17]) ).
cnf(c_6057,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_70,c_122]) ).
cnf(c_123,plain,
( ilf_type(A,member_type(power_set(B)))
| ~ ilf_type(A,subset_type(B)) ),
inference(resolve,[status(thm)],[c_70,c_6057]) ).
cnf(c_138,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_6058,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_70,c_138]) ).
cnf(c_139,plain,
( ilf_type(A,subset_type(cross_product(B,C)))
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_70,c_6058]) ).
fof(nnf_4,plain,
! [B] :
( ! [C] :
( C = B
| ? [D] :
( ( ~ member(D,C)
| ~ member(D,B) )
& ( member(D,C)
| member(D,B) )
& ilf_type(D,set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p4]) ).
fof(sk_p4_sk,plain,
! [B] :
( ! [C] :
( C = B
| ( ( ~ member(sK5(B,C),C)
| ~ member(sK5(B,C),B) )
& ( member(sK5(B,C),C)
| member(sK5(B,C),B) )
& ilf_type(sK5(B,C),set_type) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(D,sK5(B,C))],[nnf_4]) ).
fof(sk_p4,plain,
( ! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| ~ member(sK5(VAR_0,VAR_1),VAR_1)
| ~ member(sK5(VAR_0,VAR_1),VAR_0)
| ~ ilf_type(VAR_1,set_type)
| ~ ilf_type(VAR_0,set_type) )
& ! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| member(sK5(VAR_0,VAR_1),VAR_1)
| member(sK5(VAR_0,VAR_1),VAR_0)
| ~ ilf_type(VAR_1,set_type)
| ~ ilf_type(VAR_0,set_type) )
& ! [VAR_0,VAR_1] :
( VAR_1 = VAR_0
| ilf_type(sK5(VAR_0,VAR_1),set_type)
| ~ ilf_type(VAR_1,set_type)
| ~ ilf_type(VAR_0,set_type) ) ),
inference(cnf_transformation,[status(thm)],[sk_p4_sk]) ).
cnf(c_147,plain,
( B = A
| ~ member(sK5(A,B),B)
| ~ member(sK5(A,B),A)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_p4]) ).
cnf(c_6059,plain,
( A = B
| ~ member(sK5(B,A),A)
| ~ member(sK5(B,A),B)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_70,c_147]) ).
cnf(c_148,plain,
( B = A
| ~ member(sK5(A,B),B)
| ~ member(sK5(A,B),A) ),
inference(resolve,[status(thm)],[c_70,c_6059]) ).
cnf(c_149,plain,
( B = A
| member(sK5(A,B),B)
| member(sK5(A,B),A)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_p4]) ).
cnf(c_6060,plain,
( A = B
| member(sK5(B,A),A)
| member(sK5(B,A),B)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_70,c_149]) ).
cnf(c_150,plain,
( B = A
| member(sK5(A,B),B)
| member(sK5(A,B),A) ),
inference(resolve,[status(thm)],[c_70,c_6060]) ).
cnf(c_154,plain,
( member(A,domain_of(C))
| ~ member(ordered_pair(A,B),C)
| ~ ilf_type(C,binary_relation_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p3]) ).
cnf(c_6061,plain,
( member(C,domain_of(B))
| ~ member(ordered_pair(C,A),B)
| ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_70,c_154]) ).
cnf(c_155,plain,
( member(B,domain_of(A))
| ~ member(ordered_pair(B,C),A)
| ~ ilf_type(A,binary_relation_type) ),
inference(resolve,[status(thm)],[c_70,c_6061]) ).
fof(nnf_1,plain,
! [B] :
( ! [C] :
( ( ( ! [D] :
( ~ member(ordered_pair(C,D),B)
| ~ ilf_type(D,set_type) )
| member(C,domain_of(B)) )
& ( ? [X0] :
( member(ordered_pair(C,X0),B)
& ilf_type(X0,set_type) )
| ~ member(C,domain_of(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,binary_relation_type) ),
inference(fof_nnf,[status(thm)],[p1]) ).
fof(sk_p1_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,sK6(B,C)),B)
& ilf_type(sK6(B,C),set_type) )
| ~ member(C,domain_of(B)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,binary_relation_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6(B,C))],[nnf_1]) ).
fof(sk_p1,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ member(ordered_pair(VAR_1,VAR_2),VAR_0)
| ~ ilf_type(VAR_2,set_type)
| member(VAR_1,domain_of(VAR_0))
| ~ ilf_type(VAR_1,set_type)
| ~ ilf_type(VAR_0,binary_relation_type) )
& ! [VAR_0,VAR_1] :
( member(ordered_pair(VAR_1,sK6(VAR_0,VAR_1)),VAR_0)
| ~ member(VAR_1,domain_of(VAR_0))
| ~ ilf_type(VAR_1,set_type)
| ~ ilf_type(VAR_0,binary_relation_type) )
& ! [VAR_0,VAR_1] :
( ilf_type(sK6(VAR_0,VAR_1),set_type)
| ~ member(VAR_1,domain_of(VAR_0))
| ~ ilf_type(VAR_1,set_type)
| ~ ilf_type(VAR_0,binary_relation_type) ) ),
inference(cnf_transformation,[status(thm)],[sk_p1_sk]) ).
cnf(c_157,plain,
( member(ordered_pair(B,sK6(A,B)),A)
| ~ member(B,domain_of(A))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[sk_p1]) ).
cnf(c_158,plain,
( member(ordered_pair(B,sK6(A,B)),A)
| ~ member(B,domain_of(A))
| ~ ilf_type(A,binary_relation_type) ),
inference(resolve,[status(thm)],[c_70,c_157]) ).
cnf(c_180,negated_conjecture,
( domain(sK2,sK3,sK1) = sK2
| member(ordered_pair(A,sK4(A)),sK1)
| ~ member(A,sK2) ),
inference(resolve,[status(thm)],[c_70,c_65]) ).
cnf(c_181,negated_conjecture,
( domain(sK2,sK3,sK1) != sK2
| ~ member(ordered_pair(sK0,A),sK1) ),
inference(resolve,[status(thm)],[c_70,c_62]) ).
cnf(c_6062,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_70,c_50]) ).
cnf(c_6063,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_70,c_6062]) ).
cnf(c_188,plain,
( ilf_type(A,binary_relation_type)
| ~ ilf_type(A,subset_type(cross_product(B,C))) ),
inference(resolve,[status(thm)],[c_70,c_6063]) ).
cnf(c_194,plain,
ilf_type(domain(sK2,sK3,sK1),subset_type(sK2)),
inference(resolve,[status(thm)],[c_76,c_67]) ).
cnf(c_195,plain,
domain(sK2,sK3,sK1) = domain_of(sK1),
inference(resolve,[status(thm)],[c_78,c_67]) ).
cnf(c_196,plain,
ilf_type(domain_of(sK1),subset_type(sK2)),
inference(paramod,[status(thm)],[c_195,c_194]) ).
cnf(c_197,negated_conjecture,
( domain_of(sK1) != sK2
| ~ member(ordered_pair(sK0,A),sK1) ),
inference(paramod,[status(thm)],[c_195,c_181]) ).
cnf(c_198,negated_conjecture,
( domain_of(sK1) = sK2
| member(ordered_pair(A,sK4(A)),sK1)
| ~ member(A,sK2) ),
inference(paramod,[status(thm)],[c_195,c_180]) ).
cnf(c_199,negated_conjecture,
( domain_of(sK1) != sK2
| member(sK0,sK2) ),
inference(paramod,[status(thm)],[c_195,c_63]) ).
cnf(c_243,plain,
ilf_type(sK1,subset_type(cross_product(sK2,sK3))),
inference(resolve,[status(thm)],[c_139,c_67]) ).
cnf(c_313,plain,
ilf_type(domain_of(sK1),member_type(power_set(sK2))),
inference(resolve,[status(thm)],[c_196,c_123]) ).
cnf(c_328,plain,
( sK2 = A
| member(sK5(A,sK2),A)
| domain_of(sK1) = sK2
| member(ordered_pair(sK5(A,sK2),sK4(sK5(A,sK2))),sK1) ),
inference(resolve,[status(thm)],[c_198,c_150]) ).
cnf(c_345,plain,
ilf_type(sK1,binary_relation_type),
inference(resolve,[status(thm)],[c_243,c_188]) ).
cnf(c_6064,plain,
( member(domain_of(sK1),power_set(sK2))
| empty(power_set(sK2)) ),
inference(resolve,[status(thm)],[c_313,c_89]) ).
cnf(c_356,plain,
member(domain_of(sK1),power_set(sK2)),
inference(resolve,[status(thm)],[c_92,c_6064]) ).
cnf(c_363,plain,
( member(A,sK2)
| ~ member(A,domain_of(sK1)) ),
inference(resolve,[status(thm)],[c_356,c_99]) ).
cnf(c_6065,plain,
( A = domain_of(sK1)
| member(sK5(domain_of(sK1),A),A)
| member(sK5(domain_of(sK1),A),sK2) ),
inference(resolve,[status(thm)],[c_363,c_150]) ).
cnf(c_461,plain,
( domain_of(sK1) = A
| member(sK5(domain_of(sK1),A),A)
| member(sK5(domain_of(sK1),A),sK2) ),
inference(copy,[status(thm)],[c_6065]) ).
cnf(c_467,plain,
( domain_of(sK1) = sK2
| member(sK5(domain_of(sK1),sK2),sK2) ),
inference(factor,[status(thm)],[c_461]) ).
cnf(c_6066,plain,
( sK2 = domain_of(sK1)
| ~ member(sK5(domain_of(sK1),sK2),domain_of(sK1))
| domain_of(sK1) = sK2 ),
inference(resolve,[status(thm)],[c_467,c_148]) ).
cnf(c_6067,plain,
( domain_of(sK1) = sK2
| ~ member(sK5(domain_of(sK1),sK2),domain_of(sK1))
| domain_of(sK1) = sK2 ),
inference(copy,[status(thm)],[c_6066]) ).
cnf(c_1276,plain,
( ~ member(sK5(domain_of(sK1),sK2),domain_of(sK1))
| domain_of(sK1) = sK2 ),
inference(copy,[status(thm)],[c_6067]) ).
cnf(c_6068,plain,
( member(sK5(A,sK2),domain_of(sK1))
| ~ ilf_type(sK1,binary_relation_type)
| sK2 = A
| member(sK5(A,sK2),A)
| domain_of(sK1) = sK2 ),
inference(resolve,[status(thm)],[c_328,c_155]) ).
cnf(c_5938,plain,
( member(sK5(A,sK2),domain_of(sK1))
| sK2 = A
| member(sK5(A,sK2),A)
| domain_of(sK1) = sK2 ),
inference(resolve,[status(thm)],[c_345,c_6068]) ).
cnf(c_6069,plain,
( sK2 = domain_of(sK1)
| member(sK5(domain_of(sK1),sK2),domain_of(sK1))
| domain_of(sK1) = sK2 ),
inference(factor,[status(thm)],[c_5938]) ).
cnf(c_6070,plain,
( domain_of(sK1) = sK2
| member(sK5(domain_of(sK1),sK2),domain_of(sK1))
| domain_of(sK1) = sK2 ),
inference(copy,[status(thm)],[c_6069]) ).
cnf(c_5944,plain,
( member(sK5(domain_of(sK1),sK2),domain_of(sK1))
| domain_of(sK1) = sK2 ),
inference(copy,[status(thm)],[c_6070]) ).
cnf(c_6071,plain,
( domain_of(sK1) = sK2
| domain_of(sK1) = sK2 ),
inference(resolve,[status(thm)],[c_5944,c_1276]) ).
cnf(c_5945,plain,
domain_of(sK1) = sK2,
inference(copy,[status(thm)],[c_6071]) ).
cnf(c_6072,negated_conjecture,
( sK2 != sK2
| member(sK0,sK2) ),
inference(paramod,[status(thm)],[c_5945,c_199]) ).
cnf(c_6016,negated_conjecture,
member(sK0,sK2),
inference(copy,[status(thm)],[c_6072]) ).
cnf(c_6073,negated_conjecture,
( sK2 != sK2
| ~ member(ordered_pair(sK0,A),sK1) ),
inference(paramod,[status(thm)],[c_5945,c_197]) ).
cnf(c_6017,negated_conjecture,
~ member(ordered_pair(sK0,A),sK1),
inference(copy,[status(thm)],[c_6073]) ).
cnf(c_6074,plain,
( member(ordered_pair(A,sK6(sK1,A)),sK1)
| ~ member(A,domain_of(sK1)) ),
inference(resolve,[status(thm)],[c_158,c_345]) ).
cnf(c_6075,negated_conjecture,
~ member(sK0,domain_of(sK1)),
inference(resolve,[status(thm)],[c_6074,c_6017]) ).
cnf(c_6076,negated_conjecture,
~ member(sK0,sK2),
inference(paramod,[status(thm)],[c_5945,c_6075]) ).
cnf(c_6051,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_6016,c_6076]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET659+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 08:04:54 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 2394585 was started by sandbox2 on n003,
% 0.11/0.37 % Sat Sep 26 08:04:54 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 8.97/1.65
% 8.97/1.65 % given #500 (T,wt=12): 947 -member(power_set(A),power_set(B)) | member(domain_of(f4(cross_product(A,C))),B). [resolve(934,a,99,b)].
% 8.97/1.65
% 8.97/1.65 % SZS status Theorem for theBenchmark
% 8.97/1.65
% 8.97/1.65 % Proof 1 at 0.95 (+ 0.25) seconds.
% 8.97/1.65 % Length of proof is 68.
% 8.97/1.65 % Level of proof is 13.
% 8.97/1.65 % Maximum clause weight is 22.000.
% 8.97/1.65 % Given clauses 539.
% 8.97/1.65
% 8.97/1.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------