%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET025-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 11 unt; 0 def)
% Number of atoms : 11 ( 4 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 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 ( 2 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_ordered_pairs_are_small,axiom,
~ little_set(ordered_pair(a,b)),
file('theBenchmark.p',prove_ordered_pairs_are_small) ).
cnf(c_64,plain,
~ little_set(ordered_pair(a,b)),
inference(clausify,[status(thm)],[prove_ordered_pairs_are_small]) ).
fof(ordered_pair,axiom,
! [VAR_0,VAR_1] : ordered_pair(VAR_0,VAR_1) = non_ordered_pair(singleton_set(VAR_0),non_ordered_pair(VAR_0,VAR_1)),
file('theBenchmark.p',ordered_pair) ).
cnf(c_192,plain,
ordered_pair(A,B) = non_ordered_pair(singleton_set(A),non_ordered_pair(A,B)),
inference(clausify,[status(thm)],[ordered_pair]) ).
fof(singleton_set,axiom,
! [VAR_0] : singleton_set(VAR_0) = non_ordered_pair(VAR_0,VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_193,plain,
singleton_set(A) = non_ordered_pair(A,A),
inference(clausify,[status(thm)],[singleton_set]) ).
fof(non_ordered_pair4,axiom,
! [VAR_0,VAR_1] : little_set(non_ordered_pair(VAR_0,VAR_1)),
file('theBenchmark.p',non_ordered_pair4) ).
cnf(c_194,plain,
little_set(non_ordered_pair(A,B)),
inference(clausify,[status(thm)],[non_ordered_pair4]) ).
cnf(c_341,plain,
~ little_set(non_ordered_pair(singleton_set(a),non_ordered_pair(a,b))),
inference(paramod,[status(thm)],[c_192,c_64]) ).
cnf(c_342,plain,
~ little_set(non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b))),
inference(paramod,[status(thm)],[c_193,c_341]) ).
cnf(c_340,plain,
$false,
inference(resolve,[status(thm)],[c_194,c_342]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET025-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 06:56:56 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 343743 was started by sandbox on n026,
% 0.10/0.37 % Sat Sep 26 06:56:56 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.38
% 0.14/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.44
% 0.14/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.44
% 0.14/0.44 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.14/0.44 % Length of proof is 5.
% 0.14/0.44 % Level of proof is 1.
% 0.14/0.44 % Maximum clause weight is 30.000.
% 0.14/0.44 % Given clauses 0.
% 0.14/0.44
% 0.14/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------