%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET095-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 10 unt; 0 def)
% Number of atoms : 18 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_property_of_singletons2_2,axiom,
~ subclass(singleton(x),y),
file('theBenchmark.p',prove_property_of_singletons2_2) ).
cnf(c_33,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_34,plain,
member(x,y),
inference(clausify,[status(thm)],[prove_property_of_singletons2_1]) ).
fof(unordered_pair_is_subset,axiom,
! [VAR_0,VAR_1,VAR_2] :
( subclass(unordered_pair(VAR_0,VAR_2),VAR_1)
| ~ member(VAR_2,VAR_1)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',unordered_pair_is_subset) ).
cnf(c_55,plain,
( subclass(unordered_pair(A,C),B)
| ~ member(C,B)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[unordered_pair_is_subset]) ).
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]) ).
cnf(c_205,plain,
( subclass(unordered_pair(A,A),B)
| ~ member(A,B) ),
inference(factor,[status(thm)],[c_55]) ).
cnf(c_271,plain,
~ subclass(unordered_pair(x,x),y),
inference(paramod,[status(thm)],[c_159,c_33]) ).
cnf(c_476,plain,
subclass(unordered_pair(x,x),y),
inference(resolve,[status(thm)],[c_205,c_34]) ).
cnf(c_475,plain,
$false,
inference(resolve,[status(thm)],[c_271,c_476]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET095-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 07:12:12 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 1201771 was started by sandbox on n001,
% 0.08/0.35 % Sat Sep 26 07:12:12 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.40
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.40
% 0.13/0.40 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.13/0.40 % Length of proof is 8.
% 0.13/0.40 % Level of proof is 3.
% 0.13/0.40 % Maximum clause weight is 11.000.
% 0.13/0.40 % Given clauses 75.
% 0.13/0.40
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------