%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU113+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 08:45:02 AM UTC 2026
% Result : Theorem 11.36s 2.07s
% Output : CNFRefutation 11.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 14 unt; 0 def)
% Number of atoms : 70 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 67 ( 27 ~; 23 |; 10 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 49 ( 2 sgn 27 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
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(dt_k5_finsub_1,axiom,
! [A] : preboolean(finite_subsets(A)),
file('theBenchmark.p',dt_k5_finsub_1) ).
fof(fc1_finsub_1,axiom,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
file('theBenchmark.p',fc1_finsub_1) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t26_finsub_1,conjecture,
! [A] : subset(finite_subsets(A),powerset(A)),
file('theBenchmark.p',t26_finsub_1) ).
fof(t26_finsub_1_neg,negated_conjecture,
~ ! [A] : subset(finite_subsets(A),powerset(A)),
inference(assume_negation,[status(cth)],[t26_finsub_1]) ).
cnf(c_36,plain,
( subset(C,B)
| ~ in(C,A)
| finite_subsets(B) != A
| ~ preboolean(A) ),
inference(clausify,[status(thm)],[d5_finsub_1]) ).
cnf(c_42,plain,
preboolean(finite_subsets(A)),
inference(clausify,[status(thm)],[dt_k5_finsub_1]) ).
fof(nnf_7,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(sk_d3_tarski_sk,plain,
! [A,B] :
( ( ( ~ in(sK0(A,B),B)
& in(sK0(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(A,B))],[nnf_7]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ in(sK0(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK0(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,VAR_1)
| ~ in(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_tarski_sk]) ).
cnf(c_82,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_83,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_85,plain,
~ empty(powerset(A)),
inference(clausify,[status(thm)],[fc1_finsub_1]) ).
cnf(c_111,plain,
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
cnf(c_113,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(clausify,[status(thm)],[t3_subset]) ).
fof(nnf_32,plain,
? [A] : ~ subset(finite_subsets(A),powerset(A)),
inference(fof_nnf,[status(thm)],[t26_finsub_1_neg]) ).
fof(sk_t26_finsub_1_neg,plain,
~ subset(finite_subsets(sK1),powerset(sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(A,sK1)],[nnf_32]) ).
cnf(c_119,negated_conjecture,
~ subset(finite_subsets(sK1),powerset(sK1)),
inference(split_conjunct,[status(thm)],[sk_t26_finsub_1_neg]) ).
cnf(c_126,plain,
( subset(C,A)
| ~ in(C,finite_subsets(B))
| finite_subsets(A) != finite_subsets(B) ),
inference(resolve,[status(thm)],[c_42,c_36]) ).
cnf(c_240,plain,
in(sK0(finite_subsets(sK1),powerset(sK1)),finite_subsets(sK1)),
inference(resolve,[status(thm)],[c_119,c_82]) ).
cnf(c_242,negated_conjecture,
~ in(sK0(finite_subsets(sK1),powerset(sK1)),powerset(sK1)),
inference(resolve,[status(thm)],[c_83,c_119]) ).
cnf(c_257,plain,
( subset(A,B)
| ~ in(A,finite_subsets(B)) ),
inference(xxres,[status(thm)],[c_126]) ).
cnf(c_1249,plain,
subset(sK0(finite_subsets(sK1),powerset(sK1)),sK1),
inference(resolve,[status(thm)],[c_240,c_257]) ).
cnf(c_12624,plain,
( in(A,powerset(B))
| ~ element(A,powerset(B)) ),
inference(resolve,[status(thm)],[c_111,c_85]) ).
cnf(c_1265,plain,
~ element(sK0(finite_subsets(sK1),powerset(sK1)),powerset(sK1)),
inference(resolve,[status(thm)],[c_12624,c_242]) ).
cnf(c_12625,plain,
element(sK0(finite_subsets(sK1),powerset(sK1)),powerset(sK1)),
inference(resolve,[status(thm)],[c_1249,c_113]) ).
cnf(c_12623,plain,
$false,
inference(resolve,[status(thm)],[c_1265,c_12625]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU113+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n015.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 08:40:13 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 3600072 was started by sandbox on n015,
% 0.11/0.36 % Sat Sep 26 08:40:13 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 11.36/2.07
% 11.36/2.07 % given #500 (T,wt=16): 2775 in(A,powerset(B)) | -empty(A). [resolve(809,a,117,a)].
% 11.36/2.07
% 11.36/2.07 % given #1000 (A,wt=29): 491 finite_subsets(A) != c2 | in(f7(finite_subsets(B)),c2) | -subset(f7(finite_subsets(B)),A). [resolve(165,a,136,d)].
% 11.36/2.07
% 11.36/2.07 % SZS status Theorem for theBenchmark
% 11.36/2.07
% 11.36/2.07 % Proof 1 at 1.22 (+ 0.45) seconds.
% 11.36/2.07 % Length of proof is 22.
% 11.36/2.07 % Level of proof is 5.
% 11.36/2.07 % Maximum clause weight is 23.000.
% 11.36/2.07 % Given clauses 1372.
% 11.36/2.07
% 11.36/2.07 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------