%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU354+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 08:45:54 AM UTC 2026
% Result : Theorem 0.15s 6.23s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 10 unt; 0 def)
% Number of atoms : 59 ( 23 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 52 ( 22 ~; 19 |; 4 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 25 ( 1 sgn 11 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_tex_2,axiom,
! [A,B] :
( element(B,A)
=> ( proper_element(B,A)
<=> B != union(A) ) ),
file('theBenchmark.p',d2_tex_2) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t99_zfmisc_1,axiom,
! [A] : union(powerset(A)) = A,
file('theBenchmark.p',t99_zfmisc_1) ).
fof(t5_tex_2,conjecture,
! [A,B] :
( element(B,powerset(A))
=> ( proper_element(B,powerset(A))
<=> B != A ) ),
file('theBenchmark.p',t5_tex_2) ).
fof(t5_tex_2_neg,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ( proper_element(B,powerset(A))
<=> B != A ) ),
inference(assume_negation,[status(cth)],[t5_tex_2]) ).
cnf(c_45,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
cnf(c_46,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_47,plain,
element(A,powerset(A)),
inference(resolve,[status(thm)],[c_46,c_45]) ).
cnf(c_73,plain,
( union(B) != A
| ~ proper_element(A,B)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[d2_tex_2]) ).
cnf(c_74,plain,
( union(B) = A
| proper_element(A,B)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[d2_tex_2]) ).
cnf(c_106,plain,
union(powerset(A)) = A,
inference(clausify,[status(thm)],[t99_zfmisc_1]) ).
fof(nnf_43,plain,
? [A,B] :
( ( B = A
| ~ proper_element(B,powerset(A)) )
& ( B != A
| proper_element(B,powerset(A)) )
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[t5_tex_2_neg]) ).
fof(sk_t5_tex_2_neg,plain,
( ( sK0 = sK1
| ~ proper_element(sK0,powerset(sK1)) )
& ( sK0 != sK1
| proper_element(sK0,powerset(sK1)) )
& element(sK0,powerset(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_43]) ).
cnf(c_107,negated_conjecture,
element(sK0,powerset(sK1)),
inference(split_conjunct,[status(thm)],[sk_t5_tex_2_neg]) ).
cnf(c_108,negated_conjecture,
( sK0 != sK1
| proper_element(sK0,powerset(sK1)) ),
inference(split_conjunct,[status(thm)],[sk_t5_tex_2_neg]) ).
cnf(c_109,negated_conjecture,
( sK0 = sK1
| ~ proper_element(sK0,powerset(sK1)) ),
inference(split_conjunct,[status(thm)],[sk_t5_tex_2_neg]) ).
cnf(c_403,plain,
( union(powerset(A)) != A
| ~ proper_element(A,powerset(A)) ),
inference(resolve,[status(thm)],[c_73,c_47]) ).
cnf(c_404,plain,
( A != A
| ~ proper_element(A,powerset(A)) ),
inference(paramod,[status(thm)],[c_106,c_403]) ).
cnf(c_117,plain,
~ proper_element(A,powerset(A)),
inference(copy,[status(thm)],[c_404]) ).
cnf(c_405,negated_conjecture,
( union(powerset(sK1)) = sK0
| proper_element(sK0,powerset(sK1)) ),
inference(resolve,[status(thm)],[c_107,c_74]) ).
cnf(c_406,negated_conjecture,
( sK1 = sK0
| proper_element(sK0,powerset(sK1)) ),
inference(paramod,[status(thm)],[c_106,c_405]) ).
cnf(c_228,negated_conjecture,
( sK0 = sK1
| proper_element(sK0,powerset(sK1)) ),
inference(copy,[status(thm)],[c_406]) ).
cnf(c_407,negated_conjecture,
( sK0 = sK1
| sK0 = sK1 ),
inference(resolve,[status(thm)],[c_228,c_109]) ).
cnf(c_401,negated_conjecture,
sK0 = sK1,
inference(copy,[status(thm)],[c_407]) ).
cnf(c_408,negated_conjecture,
( sK0 != sK1
| proper_element(sK1,powerset(sK1)) ),
inference(paramod,[status(thm)],[c_401,c_108]) ).
cnf(c_409,negated_conjecture,
( sK1 != sK1
| proper_element(sK1,powerset(sK1)) ),
inference(paramod,[status(thm)],[c_401,c_408]) ).
cnf(c_410,negated_conjecture,
proper_element(sK1,powerset(sK1)),
inference(copy,[status(thm)],[c_409]) ).
cnf(c_402,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_117,c_410]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU354+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/6.13 % Computer : n010.cluster.edu
% 0.10/6.13 % Model : x86_64 x86_64
% 0.10/6.13 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/6.13 % Memory : 8046.5625MB
% 0.10/6.13 % OS : Linux 6.8.0-71-generic
% 0.10/6.14 % CPULimit : 300
% 0.10/6.14 % WCLimit : 300
% 0.10/6.14 % DateTime : Sat Sep 26 09:18:26 UTC 2026
% 0.10/6.14 % CPUTime :
% 0.10/6.14 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/6.14 % Process 2990137 was started by sandbox on n010,
% 0.10/6.14 % Sat Sep 26 09:18:26 2026
% 0.10/6.14 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/6.15
% 0.10/6.15 % From the command line: assign(max_seconds, 300).
% 0.15/6.23
% 0.15/6.23 % SZS status Theorem for theBenchmark
% 0.15/6.23
% 0.15/6.23 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.15/6.23 % Length of proof is 18.
% 0.15/6.23 % Level of proof is 4.
% 0.15/6.23 % Maximum clause weight is 20.000.
% 0.15/6.23 % Given clauses 215.
% 0.15/6.23
% 0.15/6.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------