%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET117+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 : n002.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 08:35:50 AM UTC 2026
% Result : Theorem 0.14s 0.64s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 16 unt; 0 def)
% Number of atoms : 32 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 8 ~; 3 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 5 sgn 11 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subclass_defn,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('theBenchmark.p',subclass_defn) ).
fof(class_elements_are_sets,axiom,
! [X] : subclass(X,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
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(corollary_1_to_ordered_pairs_are_sets,conjecture,
! [X] :
( ordered_pair(first(X),second(X)) = X
=> member(X,universal_class) ),
file('theBenchmark.p',corollary_1_to_ordered_pairs_are_sets) ).
fof(corollary_1_to_ordered_pairs_are_sets_neg,negated_conjecture,
~ ! [X] :
( ordered_pair(first(X),second(X)) = X
=> member(X,universal_class) ),
inference(assume_negation,[status(cth)],[corollary_1_to_ordered_pairs_are_sets]) ).
fof(nnf_42,plain,
? [X] :
( ~ member(X,universal_class)
& ordered_pair(first(X),second(X)) = X ),
inference(fof_nnf,[status(thm)],[corollary_1_to_ordered_pairs_are_sets_neg]) ).
fof(sk_corollary_1_to_ordered_pairs_are_sets_neg,plain,
( ~ member(sK0,universal_class)
& ordered_pair(first(sK0),second(sK0)) = sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_42]) ).
cnf(c_64,negated_conjecture,
~ member(sK0,universal_class),
inference(split_conjunct,[status(thm)],[sk_corollary_1_to_ordered_pairs_are_sets_neg]) ).
cnf(c_65,negated_conjecture,
ordered_pair(first(sK0),second(sK0)) = sK0,
inference(split_conjunct,[status(thm)],[sk_corollary_1_to_ordered_pairs_are_sets_neg]) ).
cnf(c_127,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,singleton(B))),
inference(clausify,[status(thm)],[ordered_pair_defn]) ).
cnf(c_128,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[singleton_set_defn]) ).
cnf(c_129,plain,
member(unordered_pair(A,B),universal_class),
inference(clausify,[status(thm)],[unordered_pair]) ).
cnf(c_137,plain,
subclass(A,universal_class),
inference(clausify,[status(thm)],[class_elements_are_sets]) ).
cnf(c_140,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_defn]) ).
cnf(c_417,negated_conjecture,
unordered_pair(singleton(first(sK0)),unordered_pair(first(sK0),singleton(second(sK0)))) = sK0,
inference(paramod,[status(thm)],[c_127,c_65]) ).
cnf(c_418,negated_conjecture,
unordered_pair(unordered_pair(first(sK0),first(sK0)),unordered_pair(first(sK0),singleton(second(sK0)))) = sK0,
inference(paramod,[status(thm)],[c_128,c_417]) ).
cnf(c_191,negated_conjecture,
unordered_pair(unordered_pair(first(sK0),first(sK0)),unordered_pair(first(sK0),unordered_pair(second(sK0),second(sK0)))) = sK0,
inference(paramod,[status(thm)],[c_128,c_418]) ).
cnf(c_419,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_140,c_137]) ).
cnf(c_320,negated_conjecture,
~ member(sK0,A),
inference(resolve,[status(thm)],[c_419,c_64]) ).
cnf(c_420,plain,
member(sK0,universal_class),
inference(paramod,[status(thm)],[c_191,c_129]) ).
cnf(c_416,plain,
$false,
inference(resolve,[status(thm)],[c_320,c_420]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET117+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.53 % Computer : n002.cluster.edu
% 0.09/0.53 % Model : x86_64 x86_64
% 0.09/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.53 % Memory : 8046.5625MB
% 0.09/0.53 % OS : Linux 6.8.0-71-generic
% 0.09/0.53 % CPULimit : 300
% 0.09/0.53 % WCLimit : 300
% 0.09/0.53 % DateTime : Sat Sep 26 07:12:54 UTC 2026
% 0.09/0.53 % CPUTime :
% 0.09/0.54 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.54 % Process 1090129 was started by sandbox2 on n002,
% 0.09/0.54 % Sat Sep 26 07:12:54 2026
% 0.09/0.54 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.55
% 0.09/0.55 % From the command line: assign(max_seconds, 300).
% 0.14/0.64
% 0.14/0.64 % SZS status Theorem for theBenchmark
% 0.14/0.64
% 0.14/0.64 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.14/0.64 % Length of proof is 16.
% 0.14/0.64 % Level of proof is 3.
% 0.14/0.64 % Maximum clause weight is 16.000.
% 0.14/0.64 % Given clauses 95.
% 0.14/0.64
% 0.14/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------