%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET094-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 08:35:44 AM UTC 2026
% Result : Unsatisfiable 1.05s 0.64s
% Output : CNFRefutation 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 12 unt; 0 def)
% Number of atoms : 29 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 8 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 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 : 13 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_property_of_singletons1_3,axiom,
member_of(x) != y,
file('theBenchmark.p',prove_property_of_singletons1_3) ).
cnf(c_33,plain,
member_of(x) != y,
inference(clausify,[status(thm)],[prove_property_of_singletons1_3]) ).
fof(prove_property_of_singletons1_2,axiom,
member(y,x),
file('theBenchmark.p',prove_property_of_singletons1_2) ).
cnf(c_34,plain,
member(y,x),
inference(clausify,[status(thm)],[prove_property_of_singletons1_2]) ).
fof(prove_property_of_singletons1_1,axiom,
singleton(member_of(x)) = x,
file('theBenchmark.p',prove_property_of_singletons1_1) ).
cnf(c_35,plain,
singleton(member_of(x)) = x,
inference(clausify,[status(thm)],[prove_property_of_singletons1_1]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_158,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_159,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_158]) ).
fof(unordered_pair_member,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| VAR_0 = VAR_1
| ~ member(VAR_0,unordered_pair(VAR_1,VAR_2)) ),
file('theBenchmark.p',unordered_pair_member) ).
cnf(c_163,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_member]) ).
cnf(c_270,plain,
unordered_pair(member_of(x),member_of(x)) = x,
inference(paramod,[status(thm)],[c_159,c_35]) ).
cnf(c_1194,plain,
( A = member_of(x)
| A = member_of(x)
| ~ member(A,x) ),
inference(paramod,[status(thm)],[c_270,c_163]) ).
cnf(c_1195,plain,
( A = member_of(x)
| member_of(x) = A
| ~ member(A,x) ),
inference(copy,[status(thm)],[c_1194]) ).
cnf(c_1196,plain,
( member_of(x) = A
| member_of(x) = A
| ~ member(A,x) ),
inference(copy,[status(thm)],[c_1195]) ).
cnf(c_884,plain,
( member_of(x) = A
| ~ member(A,x) ),
inference(copy,[status(thm)],[c_1196]) ).
cnf(c_1197,plain,
member_of(x) = y,
inference(resolve,[status(thm)],[c_884,c_34]) ).
cnf(c_1193,plain,
$false,
inference(resolve,[status(thm)],[c_33,c_1197]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET094-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n014.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 07:06:17 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 2464707 was started by sandbox2 on n014,
% 0.16/0.43 % Sat Sep 26 07:06:17 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 1.05/0.64
% 1.05/0.64 % SZS status Unsatisfiable for theBenchmark
% 1.05/0.64
% 1.05/0.64 % Proof 1 at 0.13 (+ 0.04) seconds.
% 1.05/0.64 % Length of proof is 9.
% 1.05/0.64 % Level of proof is 4.
% 1.05/0.64 % Maximum clause weight is 11.000.
% 1.05/0.64 % Given clauses 209.
% 1.05/0.64
% 1.05/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------