%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET647+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 : n011.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 08:36:43 AM UTC 2026
% Result : Theorem 0.24s 0.54s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 77 ( 18 unt; 0 def)
% Number of atoms : 258 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 307 ( 126 ~; 122 |; 20 &)
% ( 5 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 142 ( 4 sgn 44 !; 3 ?)
% 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)
=> ( subset(B,C)
=> ( subset(cross_product(D,B),cross_product(D,C))
& subset(cross_product(B,D),cross_product(C,D)) ) ) ) ) ),
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(p24,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( empty(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ~ member(C,B) ) ) ),
file('theBenchmark.p',p24) ).
fof(p26,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p26) ).
fof(prove_relset_1_9,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(domain_of(C),B)
=> ilf_type(C,relation_type(B,range_of(C))) ) ) ),
file('theBenchmark.p',prove_relset_1_9) ).
fof(prove_relset_1_9_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(domain_of(C),B)
=> ilf_type(C,relation_type(B,range_of(C))) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_9]) ).
fof(nnf_27,plain,
? [B] :
( ? [C] :
( ~ ilf_type(C,relation_type(B,range_of(C)))
& subset(domain_of(C),B)
& ilf_type(C,binary_relation_type) )
& ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[prove_relset_1_9_neg]) ).
fof(sk_prove_relset_1_9_neg,plain,
( ~ ilf_type(sK0,relation_type(sK1,range_of(sK0)))
& subset(domain_of(sK0),sK1)
& ilf_type(sK0,binary_relation_type)
& ilf_type(sK1,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(B,sK1),skolemize(C,sK0)],[nnf_27]) ).
cnf(c_54,negated_conjecture,
~ ilf_type(sK0,relation_type(sK1,range_of(sK0))),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_9_neg]) ).
cnf(c_55,negated_conjecture,
subset(domain_of(sK0),sK1),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_9_neg]) ).
cnf(c_56,negated_conjecture,
ilf_type(sK0,binary_relation_type),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_9_neg]) ).
cnf(c_58,plain,
ilf_type(A,set_type),
inference(clausify,[status(thm)],[p26]) ).
cnf(c_62,plain,
( ~ member(B,A)
| ~ ilf_type(B,set_type)
| ~ empty(A)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p24]) ).
cnf(c_548,plain,
( ~ member(B,A)
| ~ ilf_type(B,set_type)
| ~ empty(A) ),
inference(resolve,[status(thm)],[c_58,c_62]) ).
cnf(c_63,plain,
( ~ member(B,A)
| ~ empty(A) ),
inference(resolve,[status(thm)],[c_58,c_548]) ).
cnf(c_66,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_549,plain,
( ~ member(B,A)
| ilf_type(B,member_type(A))
| ~ ilf_type(A,set_type)
| empty(A) ),
inference(resolve,[status(thm)],[c_58,c_66]) ).
cnf(c_67,plain,
( ~ member(B,A)
| ilf_type(B,member_type(A))
| empty(A) ),
inference(resolve,[status(thm)],[c_58,c_549]) ).
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_550,plain,
( member(B,A)
| ~ ilf_type(B,member_type(A))
| ~ ilf_type(A,set_type)
| empty(A) ),
inference(resolve,[status(thm)],[c_58,c_68]) ).
cnf(c_69,plain,
( member(B,A)
| ~ ilf_type(B,member_type(A))
| empty(A) ),
inference(resolve,[status(thm)],[c_58,c_550]) ).
cnf(c_71,plain,
( ~ empty(power_set(A))
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p21]) ).
cnf(c_72,plain,
~ empty(power_set(A)),
inference(resolve,[status(thm)],[c_58,c_71]) ).
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(sK2(B,C),C)
& member(sK2(B,C),B)
& ilf_type(sK2(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,[sK2]),skolemize(D,sK2(B,C))],[nnf_20]) ).
fof(sk_p20,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK2(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(sK2(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(sK2(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_73,plain,
( ~ member(sK2(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_551,plain,
( ~ member(sK2(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(sK2(A,B),B)
| member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_58,c_551]) ).
cnf(c_75,plain,
( member(sK2(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_552,plain,
( member(sK2(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(sK2(A,B),A)
| member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_58,c_552]) ).
cnf(c_84,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_553,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_58,c_84]) ).
cnf(c_85,plain,
( ~ ilf_type(A,member_type(power_set(B)))
| ilf_type(A,subset_type(B)) ),
inference(resolve,[status(thm)],[c_58,c_553]) ).
cnf(c_95,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_554,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_58,c_95]) ).
cnf(c_555,plain,
( member(C,B)
| ~ member(C,A)
| ~ ilf_type(C,set_type)
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_58,c_554]) ).
cnf(c_96,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_58,c_555]) ).
cnf(c_112,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_556,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_58,c_112]) ).
cnf(c_113,plain,
( ilf_type(A,relation_type(B,C))
| ~ ilf_type(A,subset_type(cross_product(B,C))) ),
inference(resolve,[status(thm)],[c_58,c_556]) ).
cnf(c_116,plain,
( subset(cross_product(A,C),cross_product(B,C))
| ~ subset(A,B)
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p3]) ).
cnf(c_557,plain,
( subset(cross_product(C,B),cross_product(A,B))
| ~ subset(C,A)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_58,c_116]) ).
cnf(c_558,plain,
( subset(cross_product(B,A),cross_product(C,A))
| ~ subset(B,C)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_58,c_557]) ).
cnf(c_117,plain,
( subset(cross_product(A,C),cross_product(B,C))
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_58,c_558]) ).
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_559,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_58,c_119]) ).
cnf(c_560,plain,
( subset(B,A)
| ~ subset(C,A)
| ~ subset(B,C)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_58,c_559]) ).
cnf(c_120,plain,
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(resolve,[status(thm)],[c_58,c_560]) ).
cnf(c_153,plain,
( ilf_type(sK2(A,B),member_type(A))
| empty(A)
| member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_76,c_67]) ).
cnf(c_154,plain,
( ~ empty(A)
| member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_76,c_63]) ).
cnf(c_170,negated_conjecture,
~ ilf_type(sK0,subset_type(cross_product(sK1,range_of(sK0)))),
inference(resolve,[status(thm)],[c_113,c_54]) ).
cnf(c_174,plain,
subset(cross_product(domain_of(sK0),A),cross_product(sK1,A)),
inference(resolve,[status(thm)],[c_117,c_55]) ).
cnf(c_176,plain,
subset(sK0,cross_product(domain_of(sK0),range_of(sK0))),
inference(resolve,[status(thm)],[c_118,c_56]) ).
cnf(c_196,plain,
~ ilf_type(sK0,member_type(power_set(cross_product(sK1,range_of(sK0))))),
inference(resolve,[status(thm)],[c_85,c_170]) ).
cnf(c_561,plain,
( ~ member(A,power_set(B))
| ilf_type(A,member_type(power_set(B))) ),
inference(resolve,[status(thm)],[c_67,c_72]) ).
cnf(c_197,plain,
~ member(sK0,power_set(cross_product(sK1,range_of(sK0)))),
inference(resolve,[status(thm)],[c_561,c_196]) ).
cnf(c_198,plain,
~ member(sK2(sK0,cross_product(sK1,range_of(sK0))),cross_product(sK1,range_of(sK0))),
inference(resolve,[status(thm)],[c_74,c_197]) ).
cnf(c_232,plain,
~ empty(sK0),
inference(resolve,[status(thm)],[c_154,c_197]) ).
cnf(c_562,plain,
( ilf_type(sK2(sK0,cross_product(sK1,range_of(sK0))),member_type(sK0))
| empty(sK0) ),
inference(resolve,[status(thm)],[c_153,c_197]) ).
cnf(c_247,plain,
ilf_type(sK2(sK0,cross_product(sK1,range_of(sK0))),member_type(sK0)),
inference(resolve,[status(thm)],[c_232,c_562]) ).
cnf(c_563,plain,
( member(sK2(sK0,cross_product(sK1,range_of(sK0))),sK0)
| empty(sK0) ),
inference(resolve,[status(thm)],[c_247,c_69]) ).
cnf(c_531,plain,
member(sK2(sK0,cross_product(sK1,range_of(sK0))),sK0),
inference(resolve,[status(thm)],[c_232,c_563]) ).
cnf(c_564,plain,
( member(sK2(sK0,cross_product(sK1,range_of(sK0))),A)
| ~ subset(sK0,A) ),
inference(resolve,[status(thm)],[c_96,c_531]) ).
cnf(c_538,plain,
~ subset(sK0,cross_product(sK1,range_of(sK0))),
inference(resolve,[status(thm)],[c_564,c_198]) ).
cnf(c_565,plain,
( subset(A,cross_product(sK1,B))
| ~ subset(A,cross_product(domain_of(sK0),B)) ),
inference(resolve,[status(thm)],[c_120,c_174]) ).
cnf(c_566,plain,
~ subset(sK0,cross_product(domain_of(sK0),range_of(sK0))),
inference(resolve,[status(thm)],[c_565,c_538]) ).
cnf(c_547,plain,
$false,
inference(resolve,[status(thm)],[c_176,c_566]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET647+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n011.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 08:02:29 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 4173653 was started by sandbox on n011,
% 0.18/0.44 % Sat Sep 26 08:02:29 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.24/0.54
% 0.24/0.54 % SZS status Theorem for theBenchmark
% 0.24/0.54
% 0.24/0.54 % Proof 1 at 0.05 (+ 0.03) seconds.
% 0.24/0.54 % Length of proof is 52.
% 0.24/0.54 % Level of proof is 10.
% 0.24/0.54 % Maximum clause weight is 12.000.
% 0.24/0.54 % Given clauses 133.
% 0.24/0.54
% 0.24/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------