%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU117+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 08:45:03 AM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 8 unt; 0 def)
% Number of atoms : 46 ( 3 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 40 ( 16 ~; 11 |; 6 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 28 ( 2 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(fc2_finsub_1,axiom,
! [A] :
( preboolean(finite_subsets(A))
& diff_closed(finite_subsets(A))
& cup_closed(finite_subsets(A))
& ~ empty(finite_subsets(A)) ),
file('theBenchmark.p',fc2_finsub_1) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(d5_finsub_1,axiom,
! [A,B] :
( preboolean(B)
=> ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( finite(C)
& subset(C,A) ) ) ) ),
file('theBenchmark.p',d5_finsub_1) ).
fof(t32_finsub_1,conjecture,
! [A,B] :
( element(B,finite_subsets(A))
=> element(B,powerset(A)) ),
file('theBenchmark.p',t32_finsub_1) ).
fof(t32_finsub_1_neg,negated_conjecture,
~ ! [A,B] :
( element(B,finite_subsets(A))
=> element(B,powerset(A)) ),
inference(assume_negation,[status(cth)],[t32_finsub_1]) ).
cnf(c_37,plain,
( subset(C,B)
| ~ in(C,A)
| finite_subsets(B) != A
| ~ preboolean(A) ),
inference(clausify,[status(thm)],[d5_finsub_1]) ).
cnf(c_39,plain,
preboolean(finite_subsets(A)),
inference(clausify,[status(thm)],[fc2_finsub_1]) ).
cnf(c_64,plain,
( subset(C,A)
| ~ in(C,finite_subsets(B))
| finite_subsets(A) != finite_subsets(B) ),
inference(resolve,[status(thm)],[c_37,c_39]) ).
fof(nnf_31,plain,
? [A,B] :
( ~ element(B,powerset(A))
& element(B,finite_subsets(A)) ),
inference(fof_nnf,[status(thm)],[t32_finsub_1_neg]) ).
fof(sk_t32_finsub_1_neg,plain,
( ~ element(sK0,powerset(sK1))
& element(sK0,finite_subsets(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_31]) ).
cnf(c_66,negated_conjecture,
~ element(sK0,powerset(sK1)),
inference(split_conjunct,[status(thm)],[sk_t32_finsub_1_neg]) ).
cnf(c_67,negated_conjecture,
element(sK0,finite_subsets(sK1)),
inference(split_conjunct,[status(thm)],[sk_t32_finsub_1_neg]) ).
cnf(c_70,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
cnf(c_94,plain,
~ empty(finite_subsets(A)),
inference(clausify,[status(thm)],[fc2_finsub_1]) ).
cnf(c_102,plain,
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
cnf(c_124,negated_conjecture,
~ subset(sK0,sK1),
inference(resolve,[status(thm)],[c_70,c_66]) ).
cnf(c_214,negated_conjecture,
( in(sK0,finite_subsets(sK1))
| empty(finite_subsets(sK1)) ),
inference(resolve,[status(thm)],[c_102,c_67]) ).
cnf(c_205,negated_conjecture,
in(sK0,finite_subsets(sK1)),
inference(resolve,[status(thm)],[c_94,c_214]) ).
cnf(c_215,plain,
( subset(A,B)
| ~ in(A,finite_subsets(B)) ),
inference(xxres,[status(thm)],[c_64]) ).
cnf(c_216,plain,
~ in(sK0,finite_subsets(sK1)),
inference(resolve,[status(thm)],[c_215,c_124]) ).
cnf(c_213,plain,
$false,
inference(resolve,[status(thm)],[c_205,c_216]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU117+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.42 % Computer : n005.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Sat Sep 26 08:37:01 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.43 % Process 1712031 was started by sandbox2 on n005,
% 0.18/0.43 % Sat Sep 26 08:37:01 2026
% 0.18/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.44
% 0.18/0.44 % From the command line: assign(max_seconds, 300).
% 0.18/0.47
% 0.18/0.47 % SZS status Theorem for theBenchmark
% 0.18/0.47
% 0.18/0.47 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.18/0.47 % Length of proof is 16.
% 0.18/0.47 % Level of proof is 3.
% 0.18/0.47 % Maximum clause weight is 22.000.
% 0.18/0.47 % Given clauses 61.
% 0.18/0.47
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------