%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET094+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 08:35:44 AM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 11 unt; 0 def)
% Number of atoms : 32 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 10 ~; 4 |; 7 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 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 : 15 ( 0 sgn 8 !; 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(singleton_set_defn,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('theBenchmark.p',singleton_set_defn) ).
fof(property_of_singletons1_1,conjecture,
! [X,Y] :
( ( member(Y,X)
& singleton(member_of(X)) = X )
=> member_of(X) = Y ),
file('theBenchmark.p',property_of_singletons1_1) ).
fof(property_of_singletons1_1_neg,negated_conjecture,
~ ! [X,Y] :
( ( member(Y,X)
& singleton(member_of(X)) = X )
=> member_of(X) = Y ),
inference(assume_negation,[status(cth)],[property_of_singletons1_1]) ).
fof(nnf_46,plain,
? [X,Y] :
( member_of(X) != Y
& member(Y,X)
& singleton(member_of(X)) = X ),
inference(fof_nnf,[status(thm)],[property_of_singletons1_1_neg]) ).
fof(sk_property_of_singletons1_1_neg,plain,
( member_of(sK0) != sK1
& member(sK1,sK0)
& singleton(member_of(sK0)) = sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_46]) ).
cnf(c_68,negated_conjecture,
member_of(sK0) != sK1,
inference(split_conjunct,[status(thm)],[sk_property_of_singletons1_1_neg]) ).
cnf(c_69,negated_conjecture,
member(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_property_of_singletons1_1_neg]) ).
cnf(c_70,negated_conjecture,
singleton(member_of(sK0)) = sK0,
inference(split_conjunct,[status(thm)],[sk_property_of_singletons1_1_neg]) ).
cnf(c_137,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[singleton_set_defn]) ).
cnf(c_141,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_defn]) ).
cnf(c_205,negated_conjecture,
unordered_pair(member_of(sK0),member_of(sK0)) = sK0,
inference(paramod,[status(thm)],[c_137,c_70]) ).
cnf(c_326,negated_conjecture,
sK1 != member_of(sK0),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_327,negated_conjecture,
( sK1 = A
| ~ member(sK1,unordered_pair(member_of(sK0),A)) ),
inference(resolve,[status(thm)],[c_141,c_326]) ).
cnf(c_328,negated_conjecture,
sK1 != member_of(sK0),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_329,negated_conjecture,
~ member(sK1,unordered_pair(member_of(sK0),member_of(sK0))),
inference(resolve,[status(thm)],[c_327,c_328]) ).
cnf(c_330,negated_conjecture,
~ member(sK1,sK0),
inference(paramod,[status(thm)],[c_205,c_329]) ).
cnf(c_325,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_69,c_330]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET094+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n018.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 07:07:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 4012301 was started by sandbox2 on n018,
% 0.10/0.38 % Sat Sep 26 07:07:51 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.10/0.44
% 0.10/0.44 % SZS status Theorem for theBenchmark
% 0.10/0.44
% 0.10/0.44 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.10/0.44 % Length of proof is 10.
% 0.10/0.44 % Level of proof is 3.
% 0.10/0.44 % Maximum clause weight is 11.000.
% 0.10/0.44 % Given clauses 43.
% 0.10/0.44
% 0.10/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------