%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET650+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 : n004.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 08:36:44 AM UTC 2026
% Result : Theorem 31.17s 4.91s
% Output : CNFRefutation 31.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 97 ( 15 unt; 0 def)
% Number of atoms : 401 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 513 ( 209 ~; 224 |; 43 &)
% ( 5 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-2 aty)
% Number of variables : 229 ( 18 sgn 86 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p3,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ! [F] :
( ilf_type(F,relation_type(B,C))
=> ( member(ordered_pair(D,E),F)
=> ( member(E,C)
& member(D,B) ) ) ) ) ) ) ),
file('theBenchmark.p',p3) ).
fof(p4,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',p4) ).
fof(p6,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',p6) ).
fof(p8,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',p8) ).
fof(p10,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',p10) ).
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(p18,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',p18) ).
fof(p23,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',p23) ).
fof(p26,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p26) ).
fof(prove_relset_1_12,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(range_of(D),C)
& subset(domain_of(D),B) ) ) ) ),
file('theBenchmark.p',prove_relset_1_12) ).
fof(prove_relset_1_12_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(range_of(D),C)
& subset(domain_of(D),B) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_12]) ).
cnf(c_28,plain,
( ~ relation_like(A)
| ilf_type(A,binary_relation_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p13]) ).
cnf(c_36,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)],[p23]) ).
cnf(c_42,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_36,c_28]) ).
fof(nnf_27,plain,
? [B] :
( ? [C] :
( ? [D] :
( ( ~ subset(range_of(D),C)
| ~ subset(domain_of(D),B) )
& 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_12_neg]) ).
fof(sk_prove_relset_1_12_neg,plain,
( ( ~ subset(range_of(sK0),sK2)
| ~ subset(domain_of(sK0),sK1) )
& 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_27]) ).
cnf(c_54,negated_conjecture,
( ~ subset(range_of(sK0),sK2)
| ~ subset(domain_of(sK0),sK1) ),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_12_neg]) ).
cnf(c_55,negated_conjecture,
ilf_type(sK0,relation_type(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_12_neg]) ).
cnf(c_58,plain,
ilf_type(A,set_type),
inference(clausify,[status(thm)],[p26]) ).
fof(nnf_18,plain,
! [B] :
( ! [C] :
( ( ( ? [D] :
( ~ member(D,C)
& member(D,B)
& ilf_type(D,set_type) )
| member(B,power_set(C)) )
& ( ! [X0] :
( member(X0,C)
| ~ member(X0,B)
| ~ ilf_type(X0,set_type) )
| ~ member(B,power_set(C)) ) )
| ~ ilf_type(C,set_type) )
| ~ ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[p18]) ).
fof(sk_p18_sk,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK3(B,C),C)
& member(sK3(B,C),B)
& ilf_type(sK3(B,C),set_type) )
| member(B,power_set(C)) )
& ( ! [X0] :
( member(X0,C)
| ~ member(X0,B)
| ~ ilf_type(X0,set_type) )
| ~ member(B,power_set(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_18]) ).
fof(sk_p18,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK3(VAR_0,VAR_1),VAR_1)
| member(VAR_0,power_set(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)
| member(VAR_0,power_set(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)
| member(VAR_0,power_set(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)
| ~ member(VAR_0,power_set(VAR_1))
| ~ ilf_type(VAR_1,set_type)
| ~ ilf_type(VAR_0,set_type) ) ),
inference(cnf_transformation,[status(thm)],[sk_p18_sk]) ).
cnf(c_73,plain,
( ~ member(sK3(A,B),B)
| member(A,power_set(B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_p18]) ).
cnf(c_17793,plain,
( ~ member(sK3(B,A),A)
| member(B,power_set(A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_58,c_73]) ).
cnf(c_74,plain,
( ~ member(sK3(A,B),B)
| member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_58,c_17793]) ).
cnf(c_75,plain,
( member(sK3(A,B),A)
| member(A,power_set(B))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_p18]) ).
cnf(c_17794,plain,
( member(sK3(B,A),B)
| member(B,power_set(A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_58,c_75]) ).
cnf(c_76,plain,
( member(sK3(A,B),A)
| member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_58,c_17794]) ).
cnf(c_78,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(split_conjunct,[status(thm)],[sk_p18]) ).
cnf(c_17795,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_58,c_78]) ).
cnf(c_17796,plain,
( member(C,B)
| ~ member(C,A)
| ~ ilf_type(C,set_type)
| ~ member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_58,c_17795]) ).
cnf(c_79,plain,
( member(C,B)
| ~ member(C,A)
| ~ member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_58,c_17796]) ).
fof(nnf_10,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)],[p10]) ).
fof(sk_p10_sk,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK4(B,C),C)
& member(sK4(B,C),B)
& ilf_type(sK4(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,[sK4]),skolemize(D,sK4(B,C))],[nnf_10]) ).
fof(sk_p10,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK4(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(sK4(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(sK4(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_p10_sk]) ).
cnf(c_91,plain,
( ~ member(sK4(A,B),B)
| subset(A,B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_p10]) ).
cnf(c_17797,plain,
( ~ member(sK4(B,A),A)
| subset(B,A)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_58,c_91]) ).
cnf(c_92,plain,
( ~ member(sK4(A,B),B)
| subset(A,B) ),
inference(resolve,[status(thm)],[c_58,c_17797]) ).
cnf(c_93,plain,
( member(sK4(A,B),A)
| subset(A,B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_p10]) ).
cnf(c_17798,plain,
( member(sK4(B,A),B)
| subset(B,A)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_58,c_93]) ).
cnf(c_94,plain,
( member(sK4(A,B),A)
| subset(A,B) ),
inference(resolve,[status(thm)],[c_58,c_17798]) ).
cnf(c_100,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)],[p8]) ).
cnf(c_17799,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_58,c_100]) ).
cnf(c_101,plain,
( ilf_type(A,subset_type(cross_product(B,C)))
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_58,c_17799]) ).
fof(nnf_6,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)],[p6]) ).
fof(sk_p6_sk,plain,
! [B] :
( ! [C] :
( ( ( ! [D] :
( ~ member(ordered_pair(D,C),B)
| ~ ilf_type(D,set_type) )
| member(C,range_of(B)) )
& ( ( member(ordered_pair(sK5(B,C),C),B)
& ilf_type(sK5(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,[sK5]),skolemize(X0,sK5(B,C))],[nnf_6]) ).
fof(sk_p6,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(sK5(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(sK5(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_p6_sk]) ).
cnf(c_106,plain,
( member(ordered_pair(sK5(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_p6]) ).
cnf(c_107,plain,
( member(ordered_pair(sK5(A,B),B),A)
| ~ member(B,range_of(A))
| ~ ilf_type(A,binary_relation_type) ),
inference(resolve,[status(thm)],[c_58,c_106]) ).
fof(nnf_4,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)],[p4]) ).
fof(sk_p4_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_4]) ).
fof(sk_p4,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_p4_sk]) ).
cnf(c_111,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_p4]) ).
cnf(c_112,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_58,c_111]) ).
cnf(c_114,plain,
( member(D,B)
| ~ member(ordered_pair(C,D),E)
| ~ ilf_type(E,relation_type(A,B))
| ~ ilf_type(D,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p3]) ).
cnf(c_17800,plain,
( member(C,A)
| ~ member(ordered_pair(B,C),D)
| ~ ilf_type(D,relation_type(E,A))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_58,c_114]) ).
cnf(c_17801,plain,
( member(B,E)
| ~ member(ordered_pair(A,B),C)
| ~ ilf_type(C,relation_type(D,E))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_58,c_17800]) ).
cnf(c_17802,plain,
( member(A,D)
| ~ member(ordered_pair(E,A),B)
| ~ ilf_type(B,relation_type(C,D))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_58,c_17801]) ).
cnf(c_115,plain,
( member(E,C)
| ~ member(ordered_pair(D,E),A)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_58,c_17802]) ).
cnf(c_116,plain,
( member(C,A)
| ~ member(ordered_pair(C,D),E)
| ~ ilf_type(E,relation_type(A,B))
| ~ ilf_type(D,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p3]) ).
cnf(c_17803,plain,
( member(B,E)
| ~ member(ordered_pair(B,C),D)
| ~ ilf_type(D,relation_type(E,A))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_58,c_116]) ).
cnf(c_17804,plain,
( member(A,D)
| ~ member(ordered_pair(A,B),C)
| ~ ilf_type(C,relation_type(D,E))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_58,c_17803]) ).
cnf(c_17805,plain,
( member(E,C)
| ~ member(ordered_pair(E,A),B)
| ~ ilf_type(B,relation_type(C,D))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_58,c_17804]) ).
cnf(c_117,plain,
( member(D,B)
| ~ member(ordered_pair(D,E),A)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_58,c_17805]) ).
cnf(c_17806,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_58,c_42]) ).
cnf(c_17807,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_58,c_17806]) ).
cnf(c_152,plain,
( ilf_type(A,binary_relation_type)
| ~ ilf_type(A,subset_type(cross_product(B,C))) ),
inference(resolve,[status(thm)],[c_58,c_17807]) ).
cnf(c_167,plain,
( ~ subset(domain_of(sK0),sK1)
| member(sK4(range_of(sK0),sK2),range_of(sK0)) ),
inference(resolve,[status(thm)],[c_94,c_54]) ).
cnf(c_168,plain,
( ~ subset(range_of(sK0),sK2)
| member(sK4(domain_of(sK0),sK1),domain_of(sK0)) ),
inference(resolve,[status(thm)],[c_94,c_54]) ).
cnf(c_173,plain,
ilf_type(sK0,subset_type(cross_product(sK1,sK2))),
inference(resolve,[status(thm)],[c_101,c_55]) ).
cnf(c_177,plain,
( member(range_of(A),power_set(B))
| member(ordered_pair(sK5(A,sK3(range_of(A),B)),sK3(range_of(A),B)),A)
| ~ ilf_type(A,binary_relation_type) ),
inference(resolve,[status(thm)],[c_107,c_76]) ).
cnf(c_181,plain,
( member(domain_of(A),power_set(B))
| member(ordered_pair(sK3(domain_of(A),B),sK6(A,sK3(domain_of(A),B))),A)
| ~ ilf_type(A,binary_relation_type) ),
inference(resolve,[status(thm)],[c_112,c_76]) ).
cnf(c_184,plain,
( member(B,sK2)
| ~ member(ordered_pair(A,B),sK0) ),
inference(resolve,[status(thm)],[c_115,c_55]) ).
cnf(c_186,plain,
( member(A,sK1)
| ~ member(ordered_pair(A,B),sK0) ),
inference(resolve,[status(thm)],[c_117,c_55]) ).
cnf(c_288,plain,
( member(sK4(domain_of(sK0),sK1),domain_of(sK0))
| member(sK4(range_of(sK0),sK2),range_of(sK0)) ),
inference(resolve,[status(thm)],[c_167,c_94]) ).
cnf(c_315,plain,
ilf_type(sK0,binary_relation_type),
inference(resolve,[status(thm)],[c_173,c_152]) ).
cnf(c_330,plain,
( member(range_of(sK0),power_set(A))
| member(ordered_pair(sK5(sK0,sK3(range_of(sK0),A)),sK3(range_of(sK0),A)),sK0) ),
inference(resolve,[status(thm)],[c_177,c_315]) ).
cnf(c_448,plain,
( member(domain_of(sK0),power_set(A))
| member(ordered_pair(sK3(domain_of(sK0),A),sK6(sK0,sK3(domain_of(sK0),A))),sK0) ),
inference(resolve,[status(thm)],[c_181,c_315]) ).
cnf(c_6534,plain,
( member(sK3(range_of(sK0),A),sK2)
| member(range_of(sK0),power_set(A)) ),
inference(resolve,[status(thm)],[c_330,c_184]) ).
cnf(c_17808,plain,
( member(range_of(sK0),power_set(sK2))
| member(range_of(sK0),power_set(sK2)) ),
inference(resolve,[status(thm)],[c_6534,c_74]) ).
cnf(c_6551,plain,
member(range_of(sK0),power_set(sK2)),
inference(copy,[status(thm)],[c_17808]) ).
cnf(c_6577,plain,
( member(A,sK2)
| ~ member(A,range_of(sK0)) ),
inference(resolve,[status(thm)],[c_6551,c_79]) ).
cnf(c_6630,plain,
( member(sK4(domain_of(sK0),sK1),domain_of(sK0))
| member(sK4(range_of(sK0),sK2),sK2) ),
inference(resolve,[status(thm)],[c_6577,c_288]) ).
cnf(c_16494,plain,
( member(sK3(domain_of(sK0),A),sK1)
| member(domain_of(sK0),power_set(A)) ),
inference(resolve,[status(thm)],[c_448,c_186]) ).
cnf(c_17809,plain,
( member(domain_of(sK0),power_set(sK1))
| member(domain_of(sK0),power_set(sK1)) ),
inference(resolve,[status(thm)],[c_16494,c_74]) ).
cnf(c_16510,plain,
member(domain_of(sK0),power_set(sK1)),
inference(copy,[status(thm)],[c_17809]) ).
cnf(c_16549,plain,
( member(A,sK1)
| ~ member(A,domain_of(sK0)) ),
inference(resolve,[status(thm)],[c_16510,c_79]) ).
cnf(c_17614,plain,
( subset(range_of(sK0),sK2)
| member(sK4(domain_of(sK0),sK1),domain_of(sK0)) ),
inference(resolve,[status(thm)],[c_6630,c_92]) ).
cnf(c_17810,plain,
( member(sK4(domain_of(sK0),sK1),domain_of(sK0))
| member(sK4(domain_of(sK0),sK1),domain_of(sK0)) ),
inference(resolve,[status(thm)],[c_17614,c_168]) ).
cnf(c_17630,plain,
member(sK4(domain_of(sK0),sK1),domain_of(sK0)),
inference(copy,[status(thm)],[c_17810]) ).
cnf(c_17631,plain,
member(sK4(domain_of(sK0),sK1),sK1),
inference(resolve,[status(thm)],[c_17630,c_16549]) ).
cnf(c_17779,plain,
subset(domain_of(sK0),sK1),
inference(resolve,[status(thm)],[c_17631,c_92]) ).
cnf(c_17782,plain,
member(sK4(range_of(sK0),sK2),range_of(sK0)),
inference(resolve,[status(thm)],[c_17779,c_167]) ).
cnf(c_17783,negated_conjecture,
~ subset(range_of(sK0),sK2),
inference(resolve,[status(thm)],[c_17779,c_54]) ).
cnf(c_17784,negated_conjecture,
~ member(sK4(range_of(sK0),sK2),sK2),
inference(resolve,[status(thm)],[c_92,c_17783]) ).
cnf(c_17811,plain,
~ member(sK4(range_of(sK0),sK2),range_of(sK0)),
inference(resolve,[status(thm)],[c_6577,c_17784]) ).
cnf(c_17792,plain,
$false,
inference(resolve,[status(thm)],[c_17782,c_17811]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET650+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 08:02:53 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1185539 was started by sandbox2 on n004,
% 0.09/0.37 % Sat Sep 26 08:02:53 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 31.17/4.91
% 31.17/4.91 % given #500 (A,wt=49): 383 member(f13(range_of(A)),B) | empty(range_of(A)) | -ilf_type(A,binary_relation_type) | member(ordered_pair(f2(f6(range_of(A),B),A),f6(range_of(A),B)),A). [resolve(236,c,120,b)].
% 31.17/4.91
% 31.17/4.91 % SZS status Theorem for theBenchmark
% 31.17/4.91
% 31.17/4.91 % Proof 1 at 3.76 (+ 0.73) seconds.
% 31.17/4.91 % Length of proof is 63.
% 31.17/4.91 % Level of proof is 16.
% 31.17/4.91 % Maximum clause weight is 46.000.
% 31.17/4.91 % Given clauses 773.
% 31.17/4.91
% 31.17/4.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------