%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET813+4 : 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 : 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 08:37:00 AM UTC 2026
% Result : Theorem 2.66s 0.73s
% Output : CNFRefutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 5 unt; 0 def)
% Number of atoms : 26 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 7 ~; 4 |; 2 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 2 sgn 9 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,B)
| member(X,A) ) ),
file('theBenchmark.p',union) ).
fof(singleton,axiom,
! [X,A] :
( member(X,singleton(A))
<=> X = A ),
file('theBenchmark.p',singleton) ).
fof(successor,axiom,
! [A,X] :
( member(X,suc(A))
<=> member(X,union(A,singleton(A))) ),
file('theBenchmark.p',successor) ).
fof(thV12,conjecture,
! [A] :
( member(A,on)
=> member(A,suc(A)) ),
file('theBenchmark.p',thV12) ).
fof(thV12_neg,negated_conjecture,
~ ! [A] :
( member(A,on)
=> member(A,suc(A)) ),
inference(assume_negation,[status(cth)],[thV12]) ).
cnf(c_186,plain,
( ~ member(A,C)
| member(A,union(B,C)) ),
inference(clausify,[status(thm)],[union]) ).
cnf(c_192,plain,
( A != B
| member(A,singleton(B)) ),
inference(clausify,[status(thm)],[singleton]) ).
cnf(c_221,plain,
( ~ member(A,union(B,singleton(B)))
| member(A,suc(B)) ),
inference(clausify,[status(thm)],[successor]) ).
fof(nnf_20,plain,
? [A] :
( ~ member(A,suc(A))
& member(A,on) ),
inference(fof_nnf,[status(thm)],[thV12_neg]) ).
fof(sk_thV12_neg,plain,
( ~ member(sK0,suc(sK0))
& member(sK0,on) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_20]) ).
cnf(c_223,negated_conjecture,
~ member(sK0,suc(sK0)),
inference(split_conjunct,[status(thm)],[sk_thV12_neg]) ).
cnf(c_2412,plain,
member(A,singleton(A)),
inference(xxres,[status(thm)],[c_192]) ).
cnf(c_2547,plain,
member(A,union(B,singleton(A))),
inference(resolve,[status(thm)],[c_2412,c_186]) ).
cnf(c_2979,plain,
member(A,suc(A)),
inference(resolve,[status(thm)],[c_2547,c_221]) ).
cnf(c_2980,plain,
$false,
inference(resolve,[status(thm)],[c_2979,c_223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET813+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 08:17:32 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 1675344 was started by sandbox on n005,
% 0.09/0.35 % Sat Sep 26 08:17:32 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.36
% 0.11/0.36 % From the command line: assign(max_seconds, 300).
% 2.66/0.73
% 2.66/0.73 % SZS status Theorem for theBenchmark
% 2.66/0.73
% 2.66/0.73 % Proof 1 at 0.30 (+ 0.06) seconds.
% 2.66/0.73 % Length of proof is 12.
% 2.66/0.73 % Level of proof is 5.
% 2.66/0.73 % Maximum clause weight is 10.000.
% 2.66/0.73 % Given clauses 264.
% 2.66/0.73
% 2.66/0.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------