%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET095-6 : 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 08:35:45 AM UTC 2026
% Result : Unsatisfiable 5.11s 1.30s
% Output : CNFRefutation 5.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 13 unt; 0 def)
% Number of atoms : 29 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 10 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_property_of_singletons2_2,axiom,
~ subclass(singleton(x),y),
file('theBenchmark.p',prove_property_of_singletons2_2) ).
cnf(c_34,plain,
~ subclass(singleton(x),y),
inference(clausify,[status(thm)],[prove_property_of_singletons2_2]) ).
fof(prove_property_of_singletons2_1,axiom,
member(x,y),
file('theBenchmark.p',prove_property_of_singletons2_1) ).
cnf(c_35,plain,
member(x,y),
inference(clausify,[status(thm)],[prove_property_of_singletons2_1]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_109,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_110,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_109]) ).
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_114,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_member]) ).
fof(not_subclass_members2,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| ~ member(not_subclass_element(VAR_0,VAR_1),VAR_1) ),
file('theBenchmark.p',not_subclass_members2) ).
cnf(c_119,plain,
( subclass(A,B)
| ~ member(not_subclass_element(A,B),B) ),
inference(clausify,[status(thm)],[not_subclass_members2]) ).
fof(not_subclass_members1,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| member(not_subclass_element(VAR_0,VAR_1),VAR_0) ),
file('theBenchmark.p',not_subclass_members1) ).
cnf(c_120,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),A) ),
inference(clausify,[status(thm)],[not_subclass_members1]) ).
cnf(c_196,plain,
~ subclass(unordered_pair(x,x),y),
inference(paramod,[status(thm)],[c_110,c_34]) ).
cnf(c_197,plain,
( A = B
| ~ member(A,unordered_pair(B,B)) ),
inference(factor,[status(thm)],[c_114]) ).
cnf(c_329,plain,
member(not_subclass_element(unordered_pair(x,x),y),unordered_pair(x,x)),
inference(resolve,[status(thm)],[c_196,c_120]) ).
cnf(c_330,plain,
~ member(not_subclass_element(unordered_pair(x,x),y),y),
inference(resolve,[status(thm)],[c_119,c_196]) ).
cnf(c_4874,plain,
not_subclass_element(unordered_pair(x,x),y) = x,
inference(resolve,[status(thm)],[c_329,c_197]) ).
cnf(c_4876,plain,
~ member(x,y),
inference(paramod,[status(thm)],[c_4874,c_330]) ).
cnf(c_4875,plain,
$false,
inference(resolve,[status(thm)],[c_35,c_4876]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET095-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.56 % Computer : n001.cluster.edu
% 0.12/0.56 % Model : x86_64 x86_64
% 0.12/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.56 % Memory : 8046.5625MB
% 0.12/0.56 % OS : Linux 6.8.0-71-generic
% 0.12/0.56 % CPULimit : 300
% 0.12/0.56 % WCLimit : 300
% 0.12/0.56 % DateTime : Sat Sep 26 07:12:13 UTC 2026
% 0.12/0.57 % CPUTime :
% 0.12/0.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.57 % Process 1201899 was started by sandbox2 on n001,
% 0.12/0.57 % Sat Sep 26 07:12:13 2026
% 0.12/0.57 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.57
% 0.12/0.57 % From the command line: assign(max_seconds, 300).
% 5.11/1.30
% 5.11/1.30 % SZS status Unsatisfiable for theBenchmark
% 5.11/1.30
% 5.11/1.30 % Proof 1 at 0.57 (+ 0.14) seconds.
% 5.11/1.30 % Length of proof is 13.
% 5.11/1.30 % Level of proof is 5.
% 5.11/1.30 % Maximum clause weight is 11.000.
% 5.11/1.30 % Given clauses 483.
% 5.11/1.30
% 5.11/1.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------