%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET662+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 : n001.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 0.11s 5.56s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 10 unt; 0 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 153 ( 60 ~; 56 |; 16 &)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 71 ( 5 sgn 33 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p2,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',p2) ).
fof(p4,axiom,
! [B] :
( ilf_type(B,set_type)
=> ~ member(B,empty_set) ),
file('theBenchmark.p',p4) ).
fof(p7,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',p7) ).
fof(p12,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',p12) ).
fof(p13,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(power_set(B),set_type)
& ~ empty(power_set(B)) ) ),
file('theBenchmark.p',p13) ).
fof(p14,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',p14) ).
fof(p20,axiom,
! [B] : ilf_type(B,set_type),
file('theBenchmark.p',p20) ).
fof(prove_relset_1_25,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(empty_set,relation_type(B,C)) ) ),
file('theBenchmark.p',prove_relset_1_25) ).
fof(prove_relset_1_25_neg,negated_conjecture,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(empty_set,relation_type(B,C)) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_25]) ).
fof(nnf_20,plain,
? [B] :
( ? [C] :
( ~ ilf_type(empty_set,relation_type(B,C))
& ilf_type(C,set_type) )
& ilf_type(B,set_type) ),
inference(fof_nnf,[status(thm)],[prove_relset_1_25_neg]) ).
fof(sk_prove_relset_1_25_neg,plain,
( ~ ilf_type(empty_set,relation_type(sK0,sK1))
& ilf_type(sK1,set_type)
& ilf_type(sK0,set_type) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(B,sK0),skolemize(C,sK1)],[nnf_20]) ).
cnf(c_47,negated_conjecture,
~ ilf_type(empty_set,relation_type(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_prove_relset_1_25_neg]) ).
cnf(c_50,plain,
ilf_type(A,set_type),
inference(clausify,[status(thm)],[p20]) ).
cnf(c_54,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)],[p14]) ).
cnf(c_180,plain,
( ~ member(B,A)
| ilf_type(B,member_type(A))
| ~ ilf_type(A,set_type)
| empty(A) ),
inference(resolve,[status(thm)],[c_50,c_54]) ).
cnf(c_55,plain,
( ~ member(B,A)
| ilf_type(B,member_type(A))
| empty(A) ),
inference(resolve,[status(thm)],[c_50,c_180]) ).
cnf(c_59,plain,
( ~ empty(power_set(A))
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p13]) ).
cnf(c_60,plain,
~ empty(power_set(A)),
inference(resolve,[status(thm)],[c_50,c_59]) ).
fof(nnf_11,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)],[p12]) ).
fof(sk_p12_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_11]) ).
fof(sk_p12,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_p12_sk]) ).
cnf(c_63,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_p12]) ).
cnf(c_181,plain,
( member(sK2(B,A),B)
| member(B,power_set(A))
| ~ ilf_type(A,set_type) ),
inference(resolve,[status(thm)],[c_50,c_63]) ).
cnf(c_64,plain,
( member(sK2(A,B),A)
| member(A,power_set(B)) ),
inference(resolve,[status(thm)],[c_50,c_181]) ).
cnf(c_75,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)],[p7]) ).
cnf(c_182,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_50,c_75]) ).
cnf(c_76,plain,
( ~ ilf_type(A,member_type(power_set(B)))
| ilf_type(A,subset_type(B)) ),
inference(resolve,[status(thm)],[c_50,c_182]) ).
cnf(c_81,plain,
( ~ member(A,empty_set)
| ~ ilf_type(A,set_type) ),
inference(clausify,[status(thm)],[p4]) ).
cnf(c_82,plain,
~ member(A,empty_set),
inference(resolve,[status(thm)],[c_50,c_81]) ).
cnf(c_87,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)],[p2]) ).
cnf(c_183,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_50,c_87]) ).
cnf(c_88,plain,
( ilf_type(A,relation_type(B,C))
| ~ ilf_type(A,subset_type(cross_product(B,C))) ),
inference(resolve,[status(thm)],[c_50,c_183]) ).
cnf(c_132,plain,
member(empty_set,power_set(A)),
inference(resolve,[status(thm)],[c_82,c_64]) ).
cnf(c_135,negated_conjecture,
~ ilf_type(empty_set,subset_type(cross_product(sK0,sK1))),
inference(resolve,[status(thm)],[c_88,c_47]) ).
cnf(c_160,plain,
~ ilf_type(empty_set,member_type(power_set(cross_product(sK0,sK1)))),
inference(resolve,[status(thm)],[c_76,c_135]) ).
cnf(c_184,plain,
( ilf_type(empty_set,member_type(power_set(A)))
| empty(power_set(A)) ),
inference(resolve,[status(thm)],[c_132,c_55]) ).
cnf(c_178,plain,
ilf_type(empty_set,member_type(power_set(A))),
inference(resolve,[status(thm)],[c_60,c_184]) ).
cnf(c_179,plain,
$false,
inference(resolve,[status(thm)],[c_178,c_160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET662+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.54 % Computer : n001.cluster.edu
% 0.11/5.54 % Model : x86_64 x86_64
% 0.11/5.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.54 % Memory : 8046.5625MB
% 0.11/5.54 % OS : Linux 6.8.0-71-generic
% 0.11/5.54 % CPULimit : 300
% 0.11/5.54 % WCLimit : 300
% 0.11/5.54 % DateTime : Sat Sep 26 08:09:02 UTC 2026
% 0.11/5.54 % CPUTime :
% 0.11/5.54 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.54 % Process 1330848 was started by sandbox on n001,
% 0.11/5.54 % Sat Sep 26 08:09:02 2026
% 0.11/5.54 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.54
% 0.11/5.54 % From the command line: assign(max_seconds, 300).
% 0.11/5.56
% 0.11/5.56 % SZS status Theorem for theBenchmark
% 0.11/5.56
% 0.11/5.56 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.11/5.56 % Length of proof is 27.
% 0.11/5.56 % Level of proof is 5.
% 0.11/5.56 % Maximum clause weight is 17.000.
% 0.11/5.56 % Given clauses 33.
% 0.11/5.56
% 0.11/5.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------