%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU169+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 08:45:17 AM UTC 2026
% Result : Theorem 0.08s 0.58s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 48 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 42 ( 16 ~; 9 |; 5 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 29 ( 1 sgn 15 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('theBenchmark.p',d1_zfmisc_1) ).
fof(d2_subset_1,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('theBenchmark.p',d2_subset_1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(l3_subset_1,conjecture,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( in(C,B)
=> in(C,A) ) ),
file('theBenchmark.p',l3_subset_1) ).
fof(l3_subset_1_neg,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( in(C,B)
=> in(C,A) ) ),
inference(assume_negation,[status(cth)],[l3_subset_1]) ).
cnf(c_19,plain,
( in(B,A)
| ~ element(B,A)
| empty(A) ),
inference(clausify,[status(thm)],[d2_subset_1]) ).
fof(nnf_17,plain,
? [A,B] :
( ? [C] :
( ~ in(C,A)
& in(C,B) )
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[l3_subset_1_neg]) ).
fof(sk_l3_subset_1_neg,plain,
( ~ in(sK2,sK1)
& in(sK2,sK0)
& element(sK0,powerset(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK1),skolemize(B,sK0),skolemize(C,sK2)],[nnf_17]) ).
cnf(c_24,negated_conjecture,
element(sK0,powerset(sK1)),
inference(split_conjunct,[status(thm)],[sk_l3_subset_1_neg]) ).
cnf(c_25,negated_conjecture,
( in(sK0,powerset(sK1))
| empty(powerset(sK1)) ),
inference(resolve,[status(thm)],[c_24,c_19]) ).
cnf(c_31,negated_conjecture,
~ in(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_l3_subset_1_neg]) ).
cnf(c_32,negated_conjecture,
in(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_l3_subset_1_neg]) ).
cnf(c_41,plain,
~ empty(powerset(A)),
inference(clausify,[status(thm)],[fc1_subset_1]) ).
cnf(c_44,plain,
( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[d3_tarski]) ).
cnf(c_48,plain,
( subset(C,A)
| ~ in(C,B)
| powerset(A) != B ),
inference(clausify,[status(thm)],[d1_zfmisc_1]) ).
cnf(c_51,negated_conjecture,
in(sK0,powerset(sK1)),
inference(resolve,[status(thm)],[c_41,c_25]) ).
cnf(c_86,negated_conjecture,
( in(sK2,A)
| ~ subset(sK0,A) ),
inference(resolve,[status(thm)],[c_44,c_32]) ).
cnf(c_60,negated_conjecture,
~ subset(sK0,sK1),
inference(resolve,[status(thm)],[c_86,c_31]) ).
cnf(c_87,negated_conjecture,
( subset(sK0,A)
| powerset(A) != powerset(sK1) ),
inference(resolve,[status(thm)],[c_48,c_51]) ).
cnf(c_88,negated_conjecture,
powerset(sK1) != powerset(sK1),
inference(resolve,[status(thm)],[c_87,c_60]) ).
cnf(c_85,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU169+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.56 % Computer : n007.cluster.edu
% 0.08/0.56 % Model : x86_64 x86_64
% 0.08/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.56 % Memory : 8046.5625MB
% 0.08/0.56 % OS : Linux 6.8.0-71-generic
% 0.08/0.56 % CPULimit : 300
% 0.08/0.56 % WCLimit : 300
% 0.08/0.56 % DateTime : Sat Sep 26 08:42:10 UTC 2026
% 0.08/0.56 % CPUTime :
% 0.08/0.56 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.56 % Process 3326400 was started by sandbox2 on n007,
% 0.08/0.56 % Sat Sep 26 08:42:10 2026
% 0.08/0.56 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.57
% 0.08/0.57 % From the command line: assign(max_seconds, 300).
% 0.08/0.58
% 0.08/0.58 % SZS status Theorem for theBenchmark
% 0.08/0.58
% 0.08/0.58 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.08/0.58 % Length of proof is 16.
% 0.08/0.58 % Level of proof is 4.
% 0.08/0.58 % Maximum clause weight is 10.000.
% 0.08/0.58 % Given clauses 28.
% 0.08/0.58
% 0.08/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------