%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET101+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 : Theorem 0.17s 0.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 17 unt; 0 def)
% Number of atoms : 30 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 21 ( 13 ~; 6 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 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 : 30 ( 7 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(unordered_pair_defn,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( ( U = Y
| U = X )
& member(U,universal_class) ) ),
file('theBenchmark.p',unordered_pair_defn) ).
fof(unordered_pair,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('theBenchmark.p',unordered_pair) ).
fof(singleton_set_defn,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('theBenchmark.p',singleton_set_defn) ).
fof(ordered_pair_defn,axiom,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))),
file('theBenchmark.p',ordered_pair_defn) ).
fof(singleton_member_of_ordered_pair,conjecture,
! [X,Y] : member(singleton(X),ordered_pair(X,Y)),
file('theBenchmark.p',singleton_member_of_ordered_pair) ).
fof(singleton_member_of_ordered_pair_neg,negated_conjecture,
~ ! [X,Y] : member(singleton(X),ordered_pair(X,Y)),
inference(assume_negation,[status(cth)],[singleton_member_of_ordered_pair]) ).
fof(nnf_42,plain,
? [X,Y] : ~ member(singleton(X),ordered_pair(X,Y)),
inference(fof_nnf,[status(thm)],[singleton_member_of_ordered_pair_neg]) ).
fof(sk_singleton_member_of_ordered_pair_neg,plain,
~ member(singleton(sK0),ordered_pair(sK0,sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_42]) ).
cnf(c_64,negated_conjecture,
~ member(singleton(sK0),ordered_pair(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_singleton_member_of_ordered_pair_neg]) ).
cnf(c_126,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,singleton(B))),
inference(clausify,[status(thm)],[ordered_pair_defn]) ).
cnf(c_127,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[singleton_set_defn]) ).
cnf(c_128,plain,
member(unordered_pair(A,B),universal_class),
inference(clausify,[status(thm)],[unordered_pair]) ).
cnf(c_130,plain,
( A != B
| ~ member(A,universal_class)
| member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_defn]) ).
cnf(c_300,negated_conjecture,
~ member(unordered_pair(sK0,sK0),ordered_pair(sK0,sK1)),
inference(paramod,[status(thm)],[c_127,c_64]) ).
cnf(c_301,negated_conjecture,
~ member(unordered_pair(sK0,sK0),unordered_pair(singleton(sK0),unordered_pair(sK0,singleton(sK1)))),
inference(paramod,[status(thm)],[c_126,c_300]) ).
cnf(c_302,negated_conjecture,
~ member(unordered_pair(sK0,sK0),unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,singleton(sK1)))),
inference(paramod,[status(thm)],[c_127,c_301]) ).
cnf(c_190,negated_conjecture,
~ member(unordered_pair(sK0,sK0),unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1)))),
inference(paramod,[status(thm)],[c_127,c_302]) ).
cnf(c_303,plain,
( ~ member(singleton(A),universal_class)
| member(singleton(A),unordered_pair(unordered_pair(A,A),B)) ),
inference(resolve,[status(thm)],[c_130,c_127]) ).
cnf(c_304,plain,
( ~ member(singleton(A),universal_class)
| member(unordered_pair(A,A),unordered_pair(unordered_pair(A,A),B)) ),
inference(paramod,[status(thm)],[c_127,c_303]) ).
cnf(c_305,plain,
( ~ member(unordered_pair(A,A),universal_class)
| member(unordered_pair(A,A),unordered_pair(unordered_pair(A,A),B)) ),
inference(paramod,[status(thm)],[c_127,c_304]) ).
cnf(c_298,plain,
member(unordered_pair(A,A),unordered_pair(unordered_pair(A,A),B)),
inference(resolve,[status(thm)],[c_128,c_305]) ).
cnf(c_299,plain,
$false,
inference(resolve,[status(thm)],[c_298,c_190]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET101+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n003.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 07:09:09 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 2284573 was started by sandbox2 on n003,
% 0.17/0.44 % Sat Sep 26 07:09:09 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 0.17/0.49
% 0.17/0.49 % SZS status Theorem for theBenchmark
% 0.17/0.49
% 0.17/0.49 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.17/0.49 % Length of proof is 13.
% 0.17/0.49 % Level of proof is 3.
% 0.17/0.49 % Maximum clause weight is 48.000.
% 0.17/0.49 % Given clauses 39.
% 0.17/0.49
% 0.17/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------