%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET062+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 : n016.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 08:35:33 AM UTC 2026
% Result : Theorem 0.18s 0.69s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 9 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 34 ( 15 ~; 11 |; 6 &)
% ( 1 <=>; 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; 2 con; 0-2 aty)
% Number of variables : 24 ( 1 sgn 19 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('theBenchmark.p',subset) ).
fof(empty_set,axiom,
! [X] : ~ member(X,empty_set),
file('theBenchmark.p',empty_set) ).
fof(thI15,conjecture,
! [A] : subset(empty_set,A),
file('theBenchmark.p',thI15) ).
fof(thI15_neg,negated_conjecture,
~ ! [A] : subset(empty_set,A),
inference(assume_negation,[status(cth)],[thI15]) ).
fof(nnf_12,plain,
? [A] : ~ subset(empty_set,A),
inference(fof_nnf,[status(thm)],[thI15_neg]) ).
fof(sk_thI15_neg,plain,
~ subset(empty_set,sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_12]) ).
cnf(c_16,negated_conjecture,
~ subset(empty_set,sK0),
inference(split_conjunct,[status(thm)],[sk_thI15_neg]) ).
cnf(c_31,plain,
~ member(A,empty_set),
inference(clausify,[status(thm)],[empty_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(sK1(A,B),B)
& member(sK1(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( member(X0,B)
| ~ member(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X,sK1(A,B))],[nnf_1]) ).
fof(sk_subset,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK1(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK1(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_41,plain,
( member(sK1(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subset]) ).
cnf(c_81,negated_conjecture,
member(sK1(empty_set,sK0),empty_set),
inference(resolve,[status(thm)],[c_41,c_16]) ).
cnf(c_80,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_31,c_81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET062+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.65 % Computer : n016.cluster.edu
% 0.18/0.65 % Model : x86_64 x86_64
% 0.18/0.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.65 % Memory : 8046.5625MB
% 0.18/0.65 % OS : Linux 6.8.0-71-generic
% 0.18/0.65 % CPULimit : 300
% 0.18/0.66 % WCLimit : 300
% 0.18/0.66 % DateTime : Sat Sep 26 07:06:02 UTC 2026
% 0.18/0.66 % CPUTime :
% 0.18/0.66 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.66 % Process 247196 was started by sandbox2 on n016,
% 0.18/0.66 % Sat Sep 26 07:06:02 2026
% 0.18/0.66 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.67
% 0.18/0.67 % From the command line: assign(max_seconds, 300).
% 0.18/0.69
% 0.18/0.69 % SZS status Theorem for theBenchmark
% 0.18/0.69
% 0.18/0.69 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.18/0.69 % Length of proof is 7.
% 0.18/0.69 % Level of proof is 2.
% 0.18/0.69 % Maximum clause weight is 8.000.
% 0.18/0.69 % Given clauses 26.
% 0.18/0.69
% 0.18/0.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------