%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET660+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 : n009.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 7.07s 1.34s
% Output : CNFRefutation 7.07s
% 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 ( 13 sgn 69 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(C,range_of(B))
<=> ? [D] :
( member(ordered_pair(D,C),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(p32,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',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(range(B,C,D),subset_type(C)) ) ) ),
file('theBenchmark.p',p33) ).
fof(p34,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p34) ).
fof(prove_relset_1_23,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( ! [E] :
( ilf_type(E,set_type)
=> ( member(E,C)
=> ? [F] :
( member(ordered_pair(F,E),D)
& ilf_type(F,set_type) ) ) )
<=> range(B,C,D) = C ) ) ) ),
file('theBenchmark.p',prove_relset_1_23) ).
fof(prove_relset_1_23_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( ! [E] :
( ilf_type(E,set_type)
=> ( member(E,C)
=> ? [F] :
( member(ordered_pair(F,E),D)
& ilf_type(F,set_type) ) ) )
<=> range(B,C,D) = C ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_23]) ).
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] :
( ( range(B,C,D) != C
| ? [E] :
( ! [F] :
( ~ member(ordered_pair(F,E),D)
| ~ ilf_type(F,set_type) )
& member(E,C)
& ilf_type(E,set_type) ) )
& ( range(B,C,D) = C
| ! [X0] :
( ? [X1] :
( member(ordered_pair(X1,X0),D)
& ilf_type(X1,set_type) )
| ~ member(X0,C)
| ~ ilf_type(X0,set_type) ) )
& 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_23_neg]) ).
fof(sk_prove_relset_1_23_neg_sk,plain,
( ( range(sK2,sK3,sK1) != sK3
| ( ! [F] :
( ~ member(ordered_pair(F,sK0),sK1)
| ~ ilf_type(F,set_type) )
& member(sK0,sK3)
& ilf_type(sK0,set_type) ) )
& ( range(sK2,sK3,sK1) = sK3
| ! [X0] :
( ( member(ordered_pair(sK4(X0),X0),sK1)
& ilf_type(sK4(X0),set_type) )
| ~ member(X0,sK3)
| ~ ilf_type(X0,set_type) ) )
& ilf_type(sK1,relation_type(sK2,sK3))
& ilf_type(sK3,set_type)
& ilf_type(sK2,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK1,sK4,sK0]),skolemize(B,sK2),skolemize(C,sK3),skolemize(D,sK1),skolemize(X1,sK4(X0)),skolemize(E,sK0)],[nnf_35]) ).
fof(sk_prove_relset_1_23_neg,plain,
( ! [VAR_0] :
( range(sK2,sK3,sK1) != sK3
| ~ member(ordered_pair(VAR_0,sK0),sK1)
| ~ ilf_type(VAR_0,set_type) )
& ( range(sK2,sK3,sK1) != sK3
| member(sK0,sK3) )
& ( range(sK2,sK3,sK1) != sK3
| ilf_type(sK0,set_type) )
& ! [VAR_0] :
( range(sK2,sK3,sK1) = sK3
| member(ordered_pair(sK4(VAR_0),VAR_0),sK1)
| ~ member(VAR_0,sK3)
| ~ ilf_type(VAR_0,set_type) )
& ! [VAR_0] :
( range(sK2,sK3,sK1) = sK3
| ilf_type(sK4(VAR_0),set_type)
| ~ member(VAR_0,sK3)
| ~ ilf_type(VAR_0,set_type) )
& ilf_type(sK1,relation_type(sK2,sK3))
& ilf_type(sK3,set_type)
& ilf_type(sK2,set_type) ),
inference(cnf_transformation,[status(thm)],[sk_prove_relset_1_23_neg_sk]) ).
cnf(c_62,negated_conjecture,
( range(sK2,sK3,sK1) != sK3
| ~ member(ordered_pair(A,sK0),sK1)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_23_neg]) ).
cnf(c_63,negated_conjecture,
( range(sK2,sK3,sK1) != sK3
| member(sK0,sK3) ),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_23_neg]) ).
cnf(c_65,negated_conjecture,
( range(sK2,sK3,sK1) = sK3
| member(ordered_pair(sK4(A),A),sK1)
| ~ member(A,sK3)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_23_neg]) ).
cnf(c_67,negated_conjecture,
ilf_type(sK1,relation_type(sK2,sK3)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_23_neg]) ).
cnf(c_70,plain,
ilf_type(A,set_type),
inference(clausify,[status(thm)],[p34]) ).
cnf(c_71,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)],[p33]) ).
cnf(c_5758,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_70,c_71]) ).
cnf(c_72,plain,
( ilf_type(range(B,C,A),subset_type(C))
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_70,c_5758]) ).
cnf(c_73,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)],[p32]) ).
cnf(c_5759,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_70,c_73]) ).
cnf(c_74,plain,
( range(B,C,A) = range_of(A)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_70,c_5759]) ).
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_5760,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_5760]) ).
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_5761,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_5762,plain,
( member(C,B)
| ~ member(C,A)
| ~ ilf_type(C,set_type)
| ~ member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_70,c_5761]) ).
cnf(c_99,plain,
( member(C,B)
| ~ member(C,A)
| ~ member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_70,c_5762]) ).
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_5763,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_5763]) ).
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_5764,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_5764]) ).
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_5765,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_5765]) ).
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_5766,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_5766]) ).
cnf(c_152,plain,
( member(B,range_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_5767,plain,
( member(A,range_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_152]) ).
cnf(c_153,plain,
( member(C,range_of(A))
| ~ member(ordered_pair(B,C),A)
| ~ ilf_type(A,binary_relation_type) ),
inference(resolve,[status(thm)],[c_70,c_5767]) ).
fof(nnf_1,plain,
! [B] :
( ! [C] :
( ( ( ! [D] :
( ~ member(ordered_pair(D,C),B)
| ~ ilf_type(D,set_type) )
| member(C,range_of(B)) )
& ( ? [X0] :
( member(ordered_pair(X0,C),B)
& ilf_type(X0,set_type) )
| ~ member(C,range_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(D,C),B)
| ~ ilf_type(D,set_type) )
| member(C,range_of(B)) )
& ( ( member(ordered_pair(sK6(B,C),C),B)
& ilf_type(sK6(B,C),set_type) )
| ~ member(C,range_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_2,VAR_1),VAR_0)
| ~ ilf_type(VAR_2,set_type)
| member(VAR_1,range_of(VAR_0))
| ~ ilf_type(VAR_1,set_type)
| ~ ilf_type(VAR_0,binary_relation_type) )
& ! [VAR_0,VAR_1] :
( member(ordered_pair(sK6(VAR_0,VAR_1),VAR_1),VAR_0)
| ~ member(VAR_1,range_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,range_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(sK6(A,B),B),A)
| ~ member(B,range_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(sK6(A,B),B),A)
| ~ member(B,range_of(A))
| ~ ilf_type(A,binary_relation_type) ),
inference(resolve,[status(thm)],[c_70,c_157]) ).
cnf(c_180,negated_conjecture,
( range(sK2,sK3,sK1) = sK3
| member(ordered_pair(sK4(A),A),sK1)
| ~ member(A,sK3) ),
inference(resolve,[status(thm)],[c_70,c_65]) ).
cnf(c_181,negated_conjecture,
( range(sK2,sK3,sK1) != sK3
| ~ member(ordered_pair(A,sK0),sK1) ),
inference(resolve,[status(thm)],[c_70,c_62]) ).
cnf(c_5768,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_5769,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_5768]) ).
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_5769]) ).
cnf(c_191,plain,
ilf_type(range(sK2,sK3,sK1),subset_type(sK3)),
inference(resolve,[status(thm)],[c_72,c_67]) ).
cnf(c_192,plain,
range(sK2,sK3,sK1) = range_of(sK1),
inference(resolve,[status(thm)],[c_74,c_67]) ).
cnf(c_193,plain,
ilf_type(range_of(sK1),subset_type(sK3)),
inference(paramod,[status(thm)],[c_192,c_191]) ).
cnf(c_194,negated_conjecture,
( range_of(sK1) != sK3
| ~ member(ordered_pair(A,sK0),sK1) ),
inference(paramod,[status(thm)],[c_192,c_181]) ).
cnf(c_195,negated_conjecture,
( range_of(sK1) = sK3
| member(ordered_pair(sK4(A),A),sK1)
| ~ member(A,sK3) ),
inference(paramod,[status(thm)],[c_192,c_180]) ).
cnf(c_196,negated_conjecture,
( range_of(sK1) != sK3
| member(sK0,sK3) ),
inference(paramod,[status(thm)],[c_192,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_312,plain,
ilf_type(range_of(sK1),member_type(power_set(sK3))),
inference(resolve,[status(thm)],[c_193,c_123]) ).
cnf(c_316,plain,
( sK3 = A
| member(sK5(A,sK3),A)
| range_of(sK1) = sK3
| member(ordered_pair(sK4(sK5(A,sK3)),sK5(A,sK3)),sK1) ),
inference(resolve,[status(thm)],[c_195,c_150]) ).
cnf(c_345,plain,
ilf_type(sK1,binary_relation_type),
inference(resolve,[status(thm)],[c_243,c_188]) ).
cnf(c_5770,plain,
( member(range_of(sK1),power_set(sK3))
| empty(power_set(sK3)) ),
inference(resolve,[status(thm)],[c_312,c_89]) ).
cnf(c_347,plain,
member(range_of(sK1),power_set(sK3)),
inference(resolve,[status(thm)],[c_92,c_5770]) ).
cnf(c_354,plain,
( member(A,sK3)
| ~ member(A,range_of(sK1)) ),
inference(resolve,[status(thm)],[c_347,c_99]) ).
cnf(c_5771,plain,
( A = range_of(sK1)
| member(sK5(range_of(sK1),A),A)
| member(sK5(range_of(sK1),A),sK3) ),
inference(resolve,[status(thm)],[c_354,c_150]) ).
cnf(c_449,plain,
( range_of(sK1) = A
| member(sK5(range_of(sK1),A),A)
| member(sK5(range_of(sK1),A),sK3) ),
inference(copy,[status(thm)],[c_5771]) ).
cnf(c_455,plain,
( range_of(sK1) = sK3
| member(sK5(range_of(sK1),sK3),sK3) ),
inference(factor,[status(thm)],[c_449]) ).
cnf(c_5772,plain,
( sK3 = range_of(sK1)
| ~ member(sK5(range_of(sK1),sK3),range_of(sK1))
| range_of(sK1) = sK3 ),
inference(resolve,[status(thm)],[c_455,c_148]) ).
cnf(c_5773,plain,
( range_of(sK1) = sK3
| ~ member(sK5(range_of(sK1),sK3),range_of(sK1))
| range_of(sK1) = sK3 ),
inference(copy,[status(thm)],[c_5772]) ).
cnf(c_1239,plain,
( ~ member(sK5(range_of(sK1),sK3),range_of(sK1))
| range_of(sK1) = sK3 ),
inference(copy,[status(thm)],[c_5773]) ).
cnf(c_5774,plain,
( member(sK5(A,sK3),range_of(sK1))
| ~ ilf_type(sK1,binary_relation_type)
| sK3 = A
| member(sK5(A,sK3),A)
| range_of(sK1) = sK3 ),
inference(resolve,[status(thm)],[c_316,c_153]) ).
cnf(c_5616,plain,
( member(sK5(A,sK3),range_of(sK1))
| sK3 = A
| member(sK5(A,sK3),A)
| range_of(sK1) = sK3 ),
inference(resolve,[status(thm)],[c_345,c_5774]) ).
cnf(c_5775,plain,
( sK3 = range_of(sK1)
| member(sK5(range_of(sK1),sK3),range_of(sK1))
| range_of(sK1) = sK3 ),
inference(factor,[status(thm)],[c_5616]) ).
cnf(c_5776,plain,
( range_of(sK1) = sK3
| member(sK5(range_of(sK1),sK3),range_of(sK1))
| range_of(sK1) = sK3 ),
inference(copy,[status(thm)],[c_5775]) ).
cnf(c_5621,plain,
( member(sK5(range_of(sK1),sK3),range_of(sK1))
| range_of(sK1) = sK3 ),
inference(copy,[status(thm)],[c_5776]) ).
cnf(c_5777,plain,
( range_of(sK1) = sK3
| range_of(sK1) = sK3 ),
inference(resolve,[status(thm)],[c_5621,c_1239]) ).
cnf(c_5622,plain,
range_of(sK1) = sK3,
inference(copy,[status(thm)],[c_5777]) ).
cnf(c_5778,negated_conjecture,
( sK3 != sK3
| member(sK0,sK3) ),
inference(paramod,[status(thm)],[c_5622,c_196]) ).
cnf(c_5692,negated_conjecture,
member(sK0,sK3),
inference(copy,[status(thm)],[c_5778]) ).
cnf(c_5779,negated_conjecture,
( sK3 != sK3
| ~ member(ordered_pair(A,sK0),sK1) ),
inference(paramod,[status(thm)],[c_5622,c_194]) ).
cnf(c_5693,negated_conjecture,
~ member(ordered_pair(A,sK0),sK1),
inference(copy,[status(thm)],[c_5779]) ).
cnf(c_5780,plain,
( member(ordered_pair(sK6(sK1,A),A),sK1)
| ~ member(A,range_of(sK1)) ),
inference(resolve,[status(thm)],[c_158,c_345]) ).
cnf(c_5781,negated_conjecture,
~ member(sK0,range_of(sK1)),
inference(resolve,[status(thm)],[c_5780,c_5693]) ).
cnf(c_5782,negated_conjecture,
~ member(sK0,sK3),
inference(paramod,[status(thm)],[c_5622,c_5781]) ).
cnf(c_5757,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_5692,c_5782]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET660+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 : n009.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 08:03:16 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 3777344 was started by sandbox2 on n009,
% 0.11/0.37 % Sat Sep 26 08:03:16 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.39
% 0.15/0.39 % From the command line: assign(max_seconds, 300).
% 7.07/1.34
% 7.07/1.34 % given #500 (T,wt=12): 927 member(f8(range_of(cross_product(A,B))),B) | empty(range_of(cross_product(A,B))). [resolve(770,a,201,b)].
% 7.07/1.34
% 7.07/1.34 % SZS status Theorem for theBenchmark
% 7.07/1.34
% 7.07/1.34 % Proof 1 at 0.77 (+ 0.16) seconds.
% 7.07/1.34 % Length of proof is 68.
% 7.07/1.34 % Level of proof is 13.
% 7.07/1.34 % Maximum clause weight is 22.000.
% 7.07/1.34 % Given clauses 509.
% 7.07/1.34
% 7.07/1.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------