%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET705+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 08:36:51 AM UTC 2026
% Result : Theorem 0.18s 0.59s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 7 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 41 ( 16 ~; 16 |; 6 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 20 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('theBenchmark.p',subset) ).
fof(power_set,axiom,
! [X,A] :
( member(X,power_set(A))
<=> subset(X,A) ),
file('theBenchmark.p',power_set) ).
fof(thI48,conjecture,
! [A] : member(A,power_set(A)),
file('theBenchmark.p',thI48) ).
fof(thI48_neg,negated_conjecture,
~ ! [A] : member(A,power_set(A)),
inference(assume_negation,[status(cth)],[thI48]) ).
cnf(c_17,plain,
( ~ subset(A,B)
| member(A,power_set(B)) ),
inference(clausify,[status(thm)],[power_set]) ).
fof(nnf_1,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X0] :
( member(X0,B)
| ~ member(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[subset]) ).
fof(sk_subset_sk,plain,
! [A,B] :
( ( ( ~ member(sK0(A,B),B)
& member(sK0(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( member(X0,B)
| ~ member(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0(A,B))],[nnf_1]) ).
fof(sk_subset,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK0(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK0(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_subset_sk]) ).
cnf(c_18,plain,
( ~ member(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_19,plain,
( member(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_24,plain,
( member(A,power_set(B))
| member(sK0(A,B),A) ),
inference(resolve,[status(thm)],[c_19,c_17]) ).
cnf(c_25,plain,
( member(A,power_set(B))
| ~ member(sK0(A,B),B) ),
inference(resolve,[status(thm)],[c_18,c_17]) ).
fof(nnf_12,plain,
? [A] : ~ member(A,power_set(A)),
inference(fof_nnf,[status(thm)],[thI48_neg]) ).
fof(sk_thI48_neg,plain,
~ member(sK1,power_set(sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(A,sK1)],[nnf_12]) ).
cnf(c_47,negated_conjecture,
~ member(sK1,power_set(sK1)),
inference(split_conjunct,[status(thm)],[sk_thI48_neg]) ).
cnf(c_60,plain,
( member(A,power_set(A))
| member(A,power_set(A)) ),
inference(resolve,[status(thm)],[c_25,c_24]) ).
cnf(c_58,plain,
member(A,power_set(A)),
inference(copy,[status(thm)],[c_60]) ).
cnf(c_59,plain,
$false,
inference(resolve,[status(thm)],[c_58,c_47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET705+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.56 % Computer : n011.cluster.edu
% 0.18/0.56 % Model : x86_64 x86_64
% 0.18/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.56 % Memory : 8046.5625MB
% 0.18/0.56 % OS : Linux 6.8.0-71-generic
% 0.18/0.56 % CPULimit : 300
% 0.18/0.56 % WCLimit : 300
% 0.18/0.56 % DateTime : Sat Sep 26 08:07:15 UTC 2026
% 0.18/0.57 % CPUTime :
% 0.18/0.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.57 % Process 4181607 was started by sandbox2 on n011,
% 0.18/0.57 % Sat Sep 26 08:07:15 2026
% 0.18/0.57 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.58
% 0.18/0.58 % From the command line: assign(max_seconds, 300).
% 0.18/0.59
% 0.18/0.59 % SZS status Theorem for theBenchmark
% 0.18/0.59
% 0.18/0.59 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/0.59 % Length of proof is 11.
% 0.18/0.59 % Level of proof is 4.
% 0.18/0.59 % Maximum clause weight is 9.000.
% 0.18/0.59 % Given clauses 5.
% 0.18/0.59
% 0.18/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------