%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET668+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 : n006.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 08:36:46 AM UTC 2026
% Result : Theorem 0.66s 0.50s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 72 ( 16 unt; 0 def)
% Number of atoms : 255 ( 15 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 307 ( 124 ~; 124 |; 23 &)
% ( 5 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 139 ( 2 sgn 42 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,C))
=> ( subset(identity_relation_of(D),E)
=> ( subset(D,range(B,C,E))
& subset(D,domain(B,C,E)) ) ) ) ) ) ),
file('theBenchmark.p',p2) ).
fof(p7,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',p7) ).
fof(p9,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( B = C
<=> ( subset(C,B)
& subset(B,C) ) ) ) ),
file('theBenchmark.p',p9) ).
fof(p16,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',p16) ).
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(p29,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',p29) ).
fof(p32,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p32) ).
fof(prove_relset_1_31,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( subset(identity_relation_of(C),D)
=> ( subset(C,range(C,B,D))
& C = domain(C,B,D) ) ) ) ) ),
file('theBenchmark.p',prove_relset_1_31) ).
fof(prove_relset_1_31_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( subset(identity_relation_of(C),D)
=> ( subset(C,range(C,B,D))
& C = domain(C,B,D) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_31]) ).
fof(nnf_33,plain,
? [B] :
( ? [C] :
( ? [D] :
( ( ~ subset(C,range(C,B,D))
| domain(C,B,D) != C )
& subset(identity_relation_of(C),D)
& 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_31_neg]) ).
fof(sk_prove_relset_1_31_neg,plain,
( ( ~ subset(sK0,range(sK0,sK1,sK2))
| domain(sK0,sK1,sK2) != sK0 )
& subset(identity_relation_of(sK0),sK2)
& ilf_type(sK2,relation_type(sK0,sK1))
& ilf_type(sK0,set_type)
& ilf_type(sK1,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0,sK2]),skolemize(B,sK1),skolemize(C,sK0),skolemize(D,sK2)],[nnf_33]) ).
cnf(c_60,negated_conjecture,
( ~ subset(sK0,range(sK0,sK1,sK2))
| domain(sK0,sK1,sK2) != sK0 ),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_31_neg]) ).
cnf(c_61,negated_conjecture,
subset(identity_relation_of(sK0),sK2),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_31_neg]) ).
cnf(c_62,negated_conjecture,
ilf_type(sK2,relation_type(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_31_neg]) ).
cnf(c_65,plain,
ilf_type(A,set_type),
inference(clausify,[status(thm)],[p32]) ).
cnf(c_70,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)],[p29]) ).
cnf(c_914,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_65,c_70]) ).
cnf(c_71,plain,
( ilf_type(domain(B,C,A),subset_type(B))
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_65,c_914]) ).
cnf(c_83,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_915,plain,
( member(B,A)
| ~ ilf_type(B,member_type(A))
| ~ ilf_type(A,set_type)
| empty(A) ),
inference(resolve,[status(thm)],[c_65,c_83]) ).
cnf(c_84,plain,
( member(B,A)
| ~ ilf_type(B,member_type(A))
| empty(A) ),
inference(resolve,[status(thm)],[c_65,c_915]) ).
cnf(c_86,plain,
( ~ empty(power_set(A))
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p21]) ).
cnf(c_87,plain,
~ empty(power_set(A)),
inference(resolve,[status(thm)],[c_65,c_86]) ).
cnf(c_93,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)],[p20]) ).
cnf(c_916,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_65,c_93]) ).
cnf(c_917,plain,
( member(C,B)
| ~ member(C,A)
| ~ ilf_type(C,set_type)
| ~ member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_65,c_916]) ).
cnf(c_94,plain,
( member(C,B)
| ~ member(C,A)
| ~ member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_65,c_917]) ).
cnf(c_102,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)],[p16]) ).
cnf(c_918,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_65,c_102]) ).
cnf(c_103,plain,
( ilf_type(A,member_type(power_set(B)))
| ~ ilf_type(A,subset_type(B)) ),
inference(resolve,[status(thm)],[c_65,c_918]) ).
cnf(c_107,plain,
( ~ subset(B,A)
| ~ subset(A,B)
| B = A
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p9]) ).
cnf(c_919,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_65,c_107]) ).
cnf(c_108,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(resolve,[status(thm)],[c_65,c_919]) ).
fof(nnf_7,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)],[p7]) ).
fof(sk_p7_sk,plain,
! [B] :
( ! [C] :
( ( ( ( ~ member(sK3(B,C),C)
& member(sK3(B,C),B)
& ilf_type(sK3(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,[sK3]),skolemize(D,sK3(B,C))],[nnf_7]) ).
fof(sk_p7,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK3(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(sK3(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(sK3(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_p7_sk]) ).
cnf(c_117,plain,
( ~ member(sK3(A,B),B)
| subset(A,B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_p7]) ).
cnf(c_920,plain,
( ~ member(sK3(B,A),A)
| subset(B,A)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_65,c_117]) ).
cnf(c_118,plain,
( ~ member(sK3(A,B),B)
| subset(A,B) ),
inference(resolve,[status(thm)],[c_65,c_920]) ).
cnf(c_119,plain,
( member(sK3(A,B),A)
| subset(A,B)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(split_conjunct,[status(thm)],[sk_p7]) ).
cnf(c_921,plain,
( member(sK3(B,A),B)
| subset(B,A)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_65,c_119]) ).
cnf(c_120,plain,
( member(sK3(A,B),A)
| subset(A,B) ),
inference(resolve,[status(thm)],[c_65,c_921]) ).
cnf(c_138,plain,
( subset(C,range(A,B,D))
| ~ subset(identity_relation_of(C),D)
| ~ ilf_type(D,relation_type(A,B))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p2]) ).
cnf(c_922,plain,
( subset(B,range(D,A,C))
| ~ subset(identity_relation_of(B),C)
| ~ ilf_type(C,relation_type(D,A))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_65,c_138]) ).
cnf(c_923,plain,
( subset(A,range(C,D,B))
| ~ subset(identity_relation_of(A),B)
| ~ ilf_type(B,relation_type(C,D))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_65,c_922]) ).
cnf(c_139,plain,
( subset(D,range(B,C,A))
| ~ subset(identity_relation_of(D),A)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_65,c_923]) ).
cnf(c_140,plain,
( subset(C,domain(A,B,D))
| ~ subset(identity_relation_of(C),D)
| ~ ilf_type(D,relation_type(A,B))
| ~ ilf_type(C,set_type)
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p2]) ).
cnf(c_924,plain,
( subset(B,domain(D,A,C))
| ~ subset(identity_relation_of(B),C)
| ~ ilf_type(C,relation_type(D,A))
| ~ ilf_type(B,set_type)
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_65,c_140]) ).
cnf(c_925,plain,
( subset(A,domain(C,D,B))
| ~ subset(identity_relation_of(A),B)
| ~ ilf_type(B,relation_type(C,D))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_65,c_924]) ).
cnf(c_141,plain,
( subset(D,domain(B,C,A))
| ~ subset(identity_relation_of(D),A)
| ~ ilf_type(A,relation_type(B,C)) ),
inference(resolve,[status(thm)],[c_65,c_925]) ).
cnf(c_174,plain,
ilf_type(domain(sK0,sK1,sK2),subset_type(sK0)),
inference(resolve,[status(thm)],[c_71,c_62]) ).
cnf(c_192,plain,
( ~ subset(B,A)
| B = A
| member(sK3(A,B),A) ),
inference(resolve,[status(thm)],[c_120,c_108]) ).
cnf(c_209,plain,
( subset(sK0,range(A,B,sK2))
| ~ ilf_type(sK2,relation_type(A,B)) ),
inference(resolve,[status(thm)],[c_139,c_61]) ).
cnf(c_212,plain,
( subset(sK0,domain(A,B,sK2))
| ~ ilf_type(sK2,relation_type(A,B)) ),
inference(resolve,[status(thm)],[c_141,c_61]) ).
cnf(c_231,plain,
ilf_type(domain(sK0,sK1,sK2),member_type(power_set(sK0))),
inference(resolve,[status(thm)],[c_174,c_103]) ).
cnf(c_358,plain,
subset(sK0,range(sK0,sK1,sK2)),
inference(resolve,[status(thm)],[c_209,c_62]) ).
cnf(c_359,negated_conjecture,
domain(sK0,sK1,sK2) != sK0,
inference(resolve,[status(thm)],[c_358,c_60]) ).
cnf(c_529,plain,
subset(sK0,domain(sK0,sK1,sK2)),
inference(resolve,[status(thm)],[c_212,c_62]) ).
cnf(c_926,plain,
( sK0 = domain(sK0,sK1,sK2)
| member(sK3(domain(sK0,sK1,sK2),sK0),domain(sK0,sK1,sK2)) ),
inference(resolve,[status(thm)],[c_529,c_192]) ).
cnf(c_927,plain,
( domain(sK0,sK1,sK2) = sK0
| member(sK3(domain(sK0,sK1,sK2),sK0),domain(sK0,sK1,sK2)) ),
inference(copy,[status(thm)],[c_926]) ).
cnf(c_530,negated_conjecture,
member(sK3(domain(sK0,sK1,sK2),sK0),domain(sK0,sK1,sK2)),
inference(resolve,[status(thm)],[c_359,c_927]) ).
cnf(c_928,plain,
( ~ subset(domain(sK0,sK1,sK2),sK0)
| sK0 = domain(sK0,sK1,sK2) ),
inference(resolve,[status(thm)],[c_529,c_108]) ).
cnf(c_929,plain,
( ~ subset(domain(sK0,sK1,sK2),sK0)
| domain(sK0,sK1,sK2) = sK0 ),
inference(copy,[status(thm)],[c_928]) ).
cnf(c_532,negated_conjecture,
~ subset(domain(sK0,sK1,sK2),sK0),
inference(resolve,[status(thm)],[c_359,c_929]) ).
cnf(c_538,plain,
~ member(sK3(domain(sK0,sK1,sK2),sK0),sK0),
inference(resolve,[status(thm)],[c_118,c_532]) ).
cnf(c_930,plain,
( member(domain(sK0,sK1,sK2),power_set(sK0))
| empty(power_set(sK0)) ),
inference(resolve,[status(thm)],[c_231,c_84]) ).
cnf(c_877,plain,
member(domain(sK0,sK1,sK2),power_set(sK0)),
inference(resolve,[status(thm)],[c_87,c_930]) ).
cnf(c_931,plain,
( member(A,sK0)
| ~ member(A,domain(sK0,sK1,sK2)) ),
inference(resolve,[status(thm)],[c_94,c_877]) ).
cnf(c_932,plain,
~ member(sK3(domain(sK0,sK1,sK2),sK0),domain(sK0,sK1,sK2)),
inference(resolve,[status(thm)],[c_931,c_538]) ).
cnf(c_913,plain,
$false,
inference(resolve,[status(thm)],[c_530,c_932]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET668+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n006.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 26 08:04:04 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 783297 was started by sandbox on n006,
% 0.10/0.38 % Sat Sep 26 08:04:04 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.40
% 0.10/0.40 % From the command line: assign(max_seconds, 300).
% 0.66/0.50
% 0.66/0.50 % SZS status Theorem for theBenchmark
% 0.66/0.50
% 0.66/0.50 % Proof 1 at 0.07 (+ 0.03) seconds.
% 0.66/0.50 % Length of proof is 47.
% 0.66/0.50 % Level of proof is 8.
% 0.66/0.50 % Maximum clause weight is 26.000.
% 0.66/0.50 % Given clauses 216.
% 0.66/0.50
% 0.66/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------