%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET101-6 : 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 : n019.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 08:35:46 AM UTC 2026
% Result : Unsatisfiable 0.13s 5.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 16 unt; 0 def)
% Number of atoms : 20 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 8 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 20 ( 4 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_singleton_member_of_ordered_pair_1,axiom,
~ member(singleton(x),ordered_pair(x,y)),
file('theBenchmark.p',prove_singleton_member_of_ordered_pair_1) ).
cnf(c_34,plain,
~ member(singleton(x),ordered_pair(x,y)),
inference(clausify,[status(thm)],[prove_singleton_member_of_ordered_pair_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(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_108,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_109,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_108]) ).
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]) ).
fof(unordered_pair2,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,unordered_pair(VAR_0,VAR_1))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',unordered_pair2) ).
cnf(c_112,plain,
( member(A,unordered_pair(A,B))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair2]) ).
cnf(c_225,plain,
~ member(unordered_pair(x,x),ordered_pair(x,y)),
inference(paramod,[status(thm)],[c_109,c_34]) ).
cnf(c_226,plain,
~ member(unordered_pair(x,x),unordered_pair(singleton(x),unordered_pair(x,singleton(y)))),
inference(paramod,[status(thm)],[c_107,c_225]) ).
cnf(c_227,plain,
~ member(unordered_pair(x,x),unordered_pair(unordered_pair(x,x),unordered_pair(x,singleton(y)))),
inference(paramod,[status(thm)],[c_109,c_226]) ).
cnf(c_194,plain,
~ member(unordered_pair(x,x),unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))),
inference(paramod,[status(thm)],[c_109,c_227]) ).
cnf(c_223,plain,
member(unordered_pair(A,B),unordered_pair(unordered_pair(A,B),C)),
inference(resolve,[status(thm)],[c_112,c_110]) ).
cnf(c_224,plain,
$false,
inference(resolve,[status(thm)],[c_223,c_194]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET101-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n019.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Sat Sep 26 07:07:41 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/5.37 % Process 672177 was started by sandbox on n019,
% 0.08/5.37 % Sat Sep 26 07:07:41 2026
% 0.08/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/5.38
% 0.08/5.38 % From the command line: assign(max_seconds, 300).
% 0.13/5.42
% 0.13/5.42 % SZS status Unsatisfiable for theBenchmark
% 0.13/5.42
% 0.13/5.42 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.13/5.42 % Length of proof is 10.
% 0.13/5.42 % Level of proof is 3.
% 0.13/5.42 % Maximum clause weight is 13.000.
% 0.13/5.42 % Given clauses 27.
% 0.13/5.42
% 0.13/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------