%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET060+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 : n011.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 08:35:32 AM UTC 2026
% Result : Theorem 0.15s 0.64s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 9 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 9 ~; 3 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 19 ( 2 sgn 9 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection,axiom,
! [X,Y,Z] :
( member(Z,intersection(X,Y))
<=> ( member(Z,Y)
& member(Z,X) ) ),
file('theBenchmark.p',intersection) ).
fof(complement,axiom,
! [X,Z] :
( member(Z,complement(X))
<=> ( ~ member(Z,X)
& member(Z,universal_class) ) ),
file('theBenchmark.p',complement) ).
fof(special_classes_lemma,conjecture,
! [X,Y] : ~ member(Y,intersection(complement(X),X)),
file('theBenchmark.p',special_classes_lemma) ).
fof(special_classes_lemma_neg,negated_conjecture,
~ ! [X,Y] : ~ member(Y,intersection(complement(X),X)),
inference(assume_negation,[status(cth)],[special_classes_lemma]) ).
fof(nnf_42,plain,
? [X,Y] : member(Y,intersection(complement(X),X)),
inference(fof_nnf,[status(thm)],[special_classes_lemma_neg]) ).
fof(sk_special_classes_lemma_neg,plain,
member(sK0,intersection(complement(sK1),sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK1),skolemize(Y,sK0)],[nnf_42]) ).
cnf(c_64,negated_conjecture,
member(sK0,intersection(complement(sK1),sK1)),
inference(split_conjunct,[status(thm)],[sk_special_classes_lemma_neg]) ).
cnf(c_111,plain,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement]) ).
cnf(c_114,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection]) ).
cnf(c_115,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection]) ).
cnf(c_257,plain,
member(sK0,sK1),
inference(resolve,[status(thm)],[c_114,c_64]) ).
cnf(c_260,plain,
member(sK0,complement(sK1)),
inference(resolve,[status(thm)],[c_115,c_64]) ).
cnf(c_507,plain,
~ member(sK0,complement(sK1)),
inference(resolve,[status(thm)],[c_111,c_257]) ).
cnf(c_506,plain,
$false,
inference(resolve,[status(thm)],[c_260,c_507]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET060+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n011.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Sat Sep 26 07:00:45 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.58 % Process 4031451 was started by sandbox2 on n011,
% 0.10/0.58 % Sat Sep 26 07:00:45 2026
% 0.10/0.58 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.59
% 0.10/0.59 % From the command line: assign(max_seconds, 300).
% 0.15/0.64
% 0.15/0.64 % SZS status Theorem for theBenchmark
% 0.15/0.64
% 0.15/0.64 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.15/0.64 % Length of proof is 10.
% 0.15/0.64 % Level of proof is 3.
% 0.15/0.64 % Maximum clause weight is 21.000.
% 0.15/0.64 % Given clauses 107.
% 0.15/0.64
% 0.15/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------