%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET085-6 : 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 : n016.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 08:35:42 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.51s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 22 unt; 0 def)
% Number of atoms : 34 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 15 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 15 ( 2 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_singleton_in_unordered_pair3_4,axiom,
x != z,
file('theBenchmark.p',prove_singleton_in_unordered_pair3_4) ).
cnf(c_34,plain,
x != z,
inference(clausify,[status(thm)],[prove_singleton_in_unordered_pair3_4]) ).
cnf(c_35,plain,
z != x,
inference(copy,[status(thm)],[c_34]) ).
fof(prove_singleton_in_unordered_pair3_3,axiom,
x != y,
file('theBenchmark.p',prove_singleton_in_unordered_pair3_3) ).
cnf(c_36,plain,
x != y,
inference(clausify,[status(thm)],[prove_singleton_in_unordered_pair3_3]) ).
cnf(c_37,plain,
y != x,
inference(copy,[status(thm)],[c_36]) ).
fof(prove_singleton_in_unordered_pair3_2,axiom,
member(x,universal_class),
file('theBenchmark.p',prove_singleton_in_unordered_pair3_2) ).
cnf(c_38,plain,
member(x,universal_class),
inference(clausify,[status(thm)],[prove_singleton_in_unordered_pair3_2]) ).
fof(prove_singleton_in_unordered_pair3_1,axiom,
unordered_pair(y,z) = singleton(x),
file('theBenchmark.p',prove_singleton_in_unordered_pair3_1) ).
cnf(c_39,plain,
unordered_pair(y,z) = singleton(x),
inference(clausify,[status(thm)],[prove_singleton_in_unordered_pair3_1]) ).
cnf(c_40,plain,
singleton(x) = unordered_pair(y,z),
inference(copy,[status(thm)],[c_39]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_114,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_115,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_114]) ).
fof(unordered_pair3,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,unordered_pair(VAR_1,VAR_0))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',unordered_pair3) ).
cnf(c_117,plain,
( member(A,unordered_pair(B,A))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair3]) ).
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_119,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_member]) ).
cnf(c_243,plain,
unordered_pair(x,x) = unordered_pair(y,z),
inference(paramod,[status(thm)],[c_115,c_40]) ).
cnf(c_201,plain,
unordered_pair(y,z) = unordered_pair(x,x),
inference(copy,[status(thm)],[c_243]) ).
cnf(c_233,plain,
member(x,unordered_pair(A,x)),
inference(resolve,[status(thm)],[c_117,c_38]) ).
cnf(c_244,plain,
x != y,
inference(copy,[status(thm)],[c_37]) ).
cnf(c_245,plain,
( x = A
| ~ member(x,unordered_pair(y,A)) ),
inference(resolve,[status(thm)],[c_119,c_244]) ).
cnf(c_246,plain,
x != z,
inference(copy,[status(thm)],[c_35]) ).
cnf(c_247,plain,
~ member(x,unordered_pair(y,z)),
inference(resolve,[status(thm)],[c_245,c_246]) ).
cnf(c_248,plain,
~ member(x,unordered_pair(x,x)),
inference(paramod,[status(thm)],[c_201,c_247]) ).
cnf(c_242,plain,
$false,
inference(resolve,[status(thm)],[c_233,c_248]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET085-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n016.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 07:09:14 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 257142 was started by sandbox2 on n016,
% 0.16/0.44 % Sat Sep 26 07:09:14 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.45
% 0.16/0.45 % From the command line: assign(max_seconds, 300).
% 0.16/0.51
% 0.16/0.51 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.51
% 0.16/0.51 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.16/0.51 % Length of proof is 14.
% 0.16/0.51 % Level of proof is 3.
% 0.16/0.51 % Maximum clause weight is 11.000.
% 0.16/0.51 % Given clauses 31.
% 0.16/0.51
% 0.16/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------