%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET025-6 : 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 : n020.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 08:35:23 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.56s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 9 ( 9 unt; 0 def)
% Number of atoms : 9 ( 3 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 2 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_ordered_pair_is_set_1,axiom,
~ member(ordered_pair(x,y),universal_class),
file('theBenchmark.p',prove_ordered_pair_is_set_1) ).
cnf(c_34,plain,
~ member(ordered_pair(x,y),universal_class),
inference(clausify,[status(thm)],[prove_ordered_pair_is_set_1]) ).
fof(ordered_pair,axiom,
! [VAR_0,VAR_1] : unordered_pair(singleton(VAR_0),unordered_pair(VAR_0,singleton(VAR_1))) = ordered_pair(VAR_0,VAR_1),
file('theBenchmark.p',ordered_pair) ).
cnf(c_106,plain,
unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B),
inference(clausify,[status(thm)],[ordered_pair]) ).
cnf(c_107,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,singleton(B))),
inference(copy,[status(thm)],[c_106]) ).
fof(unordered_pairs_in_universal,axiom,
! [VAR_0,VAR_1] : member(unordered_pair(VAR_0,VAR_1),universal_class),
file('theBenchmark.p',unordered_pairs_in_universal) ).
cnf(c_110,plain,
member(unordered_pair(A,B),universal_class),
inference(clausify,[status(thm)],[unordered_pairs_in_universal]) ).
cnf(c_215,plain,
~ member(unordered_pair(singleton(x),unordered_pair(x,singleton(y))),universal_class),
inference(paramod,[status(thm)],[c_107,c_34]) ).
cnf(c_214,plain,
$false,
inference(resolve,[status(thm)],[c_110,c_215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET025-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.54 % Computer : n020.cluster.edu
% 0.09/0.54 % Model : x86_64 x86_64
% 0.09/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.54 % Memory : 8046.5625MB
% 0.09/0.54 % OS : Linux 6.8.0-71-generic
% 0.09/0.54 % CPULimit : 300
% 0.09/0.54 % WCLimit : 300
% 0.09/0.54 % DateTime : Sat Sep 26 06:55:20 UTC 2026
% 0.09/0.54 % CPUTime :
% 0.09/0.54 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.54 % Process 904564 was started by sandbox on n020,
% 0.09/0.54 % Sat Sep 26 06:55:20 2026
% 0.09/0.54 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.55
% 0.09/0.55 % From the command line: assign(max_seconds, 300).
% 0.14/0.56
% 0.14/0.56 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.56
% 0.14/0.56 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/0.56 % Length of proof is 5.
% 0.14/0.56 % Level of proof is 2.
% 0.14/0.56 % Maximum clause weight is 33.000.
% 0.14/0.56 % Given clauses 61.
% 0.14/0.56
% 0.14/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------