%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET094-6 : 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 : n001.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 0.17s 0.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 15 unt; 0 def)
% Number of atoms : 23 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 5 |; 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 : 10 ( 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_34,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_35,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_36,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_110,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_111,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_110]) ).
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_115,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_member]) ).
cnf(c_197,plain,
unordered_pair(member_of(x),member_of(x)) = x,
inference(paramod,[status(thm)],[c_111,c_36]) ).
cnf(c_235,plain,
y != member_of(x),
inference(copy,[status(thm)],[c_34]) ).
cnf(c_236,plain,
( y = A
| ~ member(y,unordered_pair(member_of(x),A)) ),
inference(resolve,[status(thm)],[c_115,c_235]) ).
cnf(c_237,plain,
y != member_of(x),
inference(copy,[status(thm)],[c_34]) ).
cnf(c_238,plain,
~ member(y,unordered_pair(member_of(x),member_of(x))),
inference(resolve,[status(thm)],[c_236,c_237]) ).
cnf(c_239,plain,
~ member(y,x),
inference(paramod,[status(thm)],[c_197,c_238]) ).
cnf(c_234,plain,
$false,
inference(resolve,[status(thm)],[c_35,c_239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET094-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n001.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 07:11:57 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 1201044 was started by sandbox2 on n001,
% 0.17/0.43 % Sat Sep 26 07:11:57 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.48
% 0.17/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.48
% 0.17/0.48 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.17/0.48 % Length of proof is 8.
% 0.17/0.48 % Level of proof is 3.
% 0.17/0.48 % Maximum clause weight is 22.000.
% 0.17/0.48 % Given clauses 30.
% 0.17/0.48
% 0.17/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------