%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET649+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 08:36:44 AM UTC 2026
% Result : Theorem 0.16s 0.34s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 67 ( 16 unt; 0 def)
% Number of atoms : 247 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 301 ( 121 ~; 115 |; 26 &)
% ( 4 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 138 ( 2 sgn 45 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( ( subset(C,D)
& subset(B,C) )
=> subset(B,D) ) ) ) ),
file('theBenchmark.p',p1) ).
fof(p2,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> subset(B,cross_product(domain_of(B),range_of(B))) ),
file('theBenchmark.p',p2) ).
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)
=> ( ( subset(D,E)
& subset(B,C) )
=> subset(cross_product(B,D),cross_product(C,E)) ) ) ) ) ),
file('theBenchmark.p',p3) ).
fof(p4,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',p4) ).
fof(p12,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',p12) ).
fof(p15,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',p15) ).
fof(p20,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',p20) ).
fof(p21,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('theBenchmark.p',p21) ).
fof(p22,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',p22) ).
fof(p26,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p26) ).
fof(prove_relset_1_11,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,binary_relation_type)
=> ( ( subset(range_of(D),C)
& subset(domain_of(D),B) )
=> ilf_type(D,relation_type(B,C)) ) ) ) ),
file('theBenchmark.p',prove_relset_1_11) ).
fof(prove_relset_1_11_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,binary_relation_type)
=> ( ( subset(range_of(D),C)
& subset(domain_of(D),B) )
=> ilf_type(D,relation_type(B,C)) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_11]) ).
fof(nnf_27,plain,
? [B] :
( ? [C] :
( ? [D] :
( ~ ilf_type(D,relation_type(B,C))
& subset(range_of(D),C)
& subset(domain_of(D),B)
& ilf_type(D,binary_relation_type) )
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[prove_relset_1_11_neg]) ).
fof(sk_prove_relset_1_11_neg,plain,
( ~ ilf_type(sK0,relation_type(sK1,sK2))
& subset(range_of(sK0),sK2)
& subset(domain_of(sK0),sK1)
& ilf_type(sK0,binary_relation_type)
& 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,
~ ilf_type(sK0,relation_type(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_11_neg]) ).
cnf(c_55,negated_conjecture,
subset(range_of(sK0),sK2),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_11_neg]) ).
cnf(c_56,negated_conjecture,
subset(domain_of(sK0),sK1),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_11_neg]) ).
cnf(c_57,negated_conjecture,
ilf_type(sK0,binary_relation_type),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_11_neg]) ).
cnf(c_60,plain,
ilf_type(A,set_type),
inference(clausify,[status(thm)],[p26]) ).
cnf(c_68,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)],[p22]) ).
cnf(c_578,plain,
( ~ member(B,A)
| ilf_type(B,member_type(A))
| ~ ilf_type(A,set_type)
| empty(A) ),
inference(resolve,[status(thm)],[c_60,c_68]) ).
cnf(c_69,plain,
( ~ member(B,A)
| ilf_type(B,member_type(A))
| empty(A) ),
inference(resolve,[status(thm)],[c_60,c_578]) ).
cnf(c_73,plain,
( ~ empty(power_set(A))
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p21]) ).
cnf(c_74,plain,
~ empty(power_set(A)),
inference(resolve,[status(thm)],[c_60,c_73]) ).
fof(nnf_20,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)],[p20]) ).
fof(sk_p20_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_20]) ).
fof(sk_p20,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_p20_sk]) ).
cnf(c_75,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_p20]) ).
cnf(c_579,plain,
( ~ member(sK3(B,A),A)
| member(B,power_set(A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_75]) ).
cnf(c_76,plain,
( ~ member(sK3(A,B),B)
| member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_60,c_579]) ).
cnf(c_77,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_p20]) ).
cnf(c_580,plain,
( member(sK3(B,A),B)
| member(B,power_set(A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_77]) ).
cnf(c_78,plain,
( member(sK3(A,B),A)
| member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_60,c_580]) ).
cnf(c_86,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)],[p15]) ).
cnf(c_581,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_60,c_86]) ).
cnf(c_87,plain,
( ~ ilf_type(A,member_type(power_set(B)))
| ilf_type(A,subset_type(B)) ),
inference(resolve,[status(thm)],[c_60,c_581]) ).
cnf(c_97,plain,
( member(C,B)
| ~ member(C,A)
| ~ ilf_type(C,set_type)
| ~ subset(A,B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p12]) ).
cnf(c_582,plain,
( member(C,A)
| ~ member(C,B)
| ~ ilf_type(C,set_type)
| ~ subset(B,A)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_97]) ).
cnf(c_583,plain,
( member(C,B)
| ~ member(C,A)
| ~ ilf_type(C,set_type)
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_60,c_582]) ).
cnf(c_98,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_60,c_583]) ).
cnf(c_114,plain,
( ilf_type(C,relation_type(A,B))
| ~ ilf_type(C,subset_type(cross_product(A,B)))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p4]) ).
cnf(c_584,plain,
( ilf_type(B,relation_type(C,A))
| ~ ilf_type(B,subset_type(cross_product(C,A)))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_114]) ).
cnf(c_115,plain,
( ilf_type(A,relation_type(B,C))
| ~ ilf_type(A,subset_type(cross_product(B,C))) ),
inference(resolve,[status(thm)],[c_60,c_584]) ).
cnf(c_116,plain,
( subset(cross_product(A,C),cross_product(B,D))
| ~ subset(C,D)
| ~ subset(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_585,plain,
( subset(cross_product(D,B),cross_product(A,C))
| ~ subset(B,C)
| ~ subset(D,A)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_116]) ).
cnf(c_586,plain,
( subset(cross_product(C,A),cross_product(D,B))
| ~ subset(A,B)
| ~ subset(C,D)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_585]) ).
cnf(c_587,plain,
( subset(cross_product(B,D),cross_product(C,A))
| ~ subset(D,A)
| ~ subset(B,C)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_586]) ).
cnf(c_117,plain,
( subset(cross_product(A,C),cross_product(B,D))
| ~ subset(C,D)
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_60,c_587]) ).
cnf(c_118,plain,
( subset(A,cross_product(domain_of(A),range_of(A)))
| ~ ilf_type(A,binary_relation_type) ),
inference(clausify,[status(thm)],[p2]) ).
cnf(c_119,plain,
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p1]) ).
cnf(c_588,plain,
( subset(C,B)
| ~ subset(A,B)
| ~ subset(C,A)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_119]) ).
cnf(c_589,plain,
( subset(B,A)
| ~ subset(C,A)
| ~ subset(B,C)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_60,c_588]) ).
cnf(c_120,plain,
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_60,c_589]) ).
cnf(c_166,plain,
( member(A,power_set(C))
| member(sK3(A,C),B)
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_98,c_78]) ).
cnf(c_182,negated_conjecture,
~ ilf_type(sK0,subset_type(cross_product(sK1,sK2))),
inference(resolve,[status(thm)],[c_115,c_54]) ).
cnf(c_192,plain,
subset(sK0,cross_product(domain_of(sK0),range_of(sK0))),
inference(resolve,[status(thm)],[c_118,c_57]) ).
cnf(c_225,plain,
~ ilf_type(sK0,member_type(power_set(cross_product(sK1,sK2)))),
inference(resolve,[status(thm)],[c_87,c_182]) ).
cnf(c_590,plain,
( ~ member(A,power_set(B))
| ilf_type(A,member_type(power_set(B))) ),
inference(resolve,[status(thm)],[c_69,c_74]) ).
cnf(c_226,plain,
~ member(sK0,power_set(cross_product(sK1,sK2))),
inference(resolve,[status(thm)],[c_590,c_225]) ).
cnf(c_227,plain,
~ member(sK3(sK0,cross_product(sK1,sK2)),cross_product(sK1,sK2)),
inference(resolve,[status(thm)],[c_76,c_226]) ).
cnf(c_591,plain,
( member(sK0,power_set(cross_product(sK1,sK2)))
| ~ subset(sK0,cross_product(sK1,sK2)) ),
inference(resolve,[status(thm)],[c_166,c_227]) ).
cnf(c_484,plain,
~ subset(sK0,cross_product(sK1,sK2)),
inference(resolve,[status(thm)],[c_591,c_226]) ).
cnf(c_592,plain,
( subset(sK0,A)
| ~ subset(cross_product(domain_of(sK0),range_of(sK0)),A) ),
inference(resolve,[status(thm)],[c_120,c_192]) ).
cnf(c_546,plain,
~ subset(cross_product(domain_of(sK0),range_of(sK0)),cross_product(sK1,sK2)),
inference(resolve,[status(thm)],[c_592,c_484]) ).
cnf(c_593,negated_conjecture,
( subset(cross_product(A,range_of(sK0)),cross_product(B,sK2))
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_117,c_55]) ).
cnf(c_594,negated_conjecture,
~ subset(domain_of(sK0),sK1),
inference(resolve,[status(thm)],[c_593,c_546]) ).
cnf(c_577,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_56,c_594]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET649+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sat Sep 26 08:02:36 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.30 % Process 84383 was started by sandbox on n012,
% 0.04/0.30 % Sat Sep 26 08:02:36 2026
% 0.04/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.04/0.30
% 0.04/0.30 % From the command line: assign(max_seconds, 300).
% 0.16/0.34
% 0.16/0.34 % SZS status Theorem for theBenchmark
% 0.16/0.34
% 0.16/0.34 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.16/0.34 % Length of proof is 44.
% 0.16/0.34 % Level of proof is 9.
% 0.16/0.34 % Maximum clause weight is 27.000.
% 0.16/0.34 % Given clauses 136.
% 0.16/0.34
% 0.16/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------