%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET581+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 08:36:31 AM UTC 2026
% Result : Theorem 0.16s 0.45s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 10 unt; 0 def)
% Number of atoms : 34 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 10 ~; 4 |; 7 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 1 sgn 12 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('theBenchmark.p',intersection_defn) ).
fof(empty_set_defn,axiom,
! [B] : ~ member(B,empty_set),
file('theBenchmark.p',empty_set_defn) ).
fof(not_equal_defn,axiom,
! [B,C] :
( not_equal(B,C)
<=> B != C ),
file('theBenchmark.p',not_equal_defn) ).
fof(prove_th24,conjecture,
! [B,C,D] :
( ( member(B,D)
& member(B,C) )
=> not_equal(intersection(C,D),empty_set) ),
file('theBenchmark.p',prove_th24) ).
fof(prove_th24_neg,negated_conjecture,
~ ! [B,C,D] :
( ( member(B,D)
& member(B,C) )
=> not_equal(intersection(C,D),empty_set) ),
inference(assume_negation,[status(cth)],[prove_th24]) ).
fof(nnf_7,plain,
? [B,C,D] :
( ~ not_equal(intersection(C,D),empty_set)
& member(B,D)
& member(B,C) ),
inference(fof_nnf,[status(thm)],[prove_th24_neg]) ).
fof(sk_prove_th24_neg,plain,
( ~ not_equal(intersection(sK0,sK1),empty_set)
& member(sK2,sK1)
& member(sK2,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1]),skolemize(B,sK2),skolemize(C,sK0),skolemize(D,sK1)],[nnf_7]) ).
cnf(c_11,negated_conjecture,
~ not_equal(intersection(sK0,sK1),empty_set),
inference(split_conjunct,[status(thm)],[sk_prove_th24_neg]) ).
cnf(c_12,negated_conjecture,
member(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_th24_neg]) ).
cnf(c_13,negated_conjecture,
member(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_prove_th24_neg]) ).
cnf(c_15,plain,
( B = A
| not_equal(A,B) ),
inference(clausify,[status(thm)],[not_equal_defn]) ).
cnf(c_21,plain,
~ member(A,empty_set),
inference(clausify,[status(thm)],[empty_set_defn]) ).
cnf(c_22,plain,
( ~ member(A,C)
| ~ member(A,B)
| member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection_defn]) ).
cnf(c_60,negated_conjecture,
empty_set = intersection(sK0,sK1),
inference(resolve,[status(thm)],[c_15,c_11]) ).
cnf(c_28,negated_conjecture,
intersection(sK0,sK1) = empty_set,
inference(copy,[status(thm)],[c_60]) ).
cnf(c_61,negated_conjecture,
( ~ member(sK2,A)
| member(sK2,intersection(sK0,A)) ),
inference(resolve,[status(thm)],[c_22,c_13]) ).
cnf(c_62,negated_conjecture,
member(sK2,intersection(sK0,sK1)),
inference(resolve,[status(thm)],[c_61,c_12]) ).
cnf(c_63,negated_conjecture,
member(sK2,empty_set),
inference(paramod,[status(thm)],[c_28,c_62]) ).
cnf(c_59,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_21,c_63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET581+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n013.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 07:56:37 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 2275543 was started by sandbox2 on n013,
% 0.16/0.42 % Sat Sep 26 07:56:37 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 0.16/0.45
% 0.16/0.45 % Assigning unary symbol f2 kb_weight 0 and highest precedence (10).
% 0.16/0.45
% 0.16/0.45 % SZS status Theorem for theBenchmark
% 0.16/0.45
% 0.16/0.45 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.16/0.45 % Length of proof is 12.
% 0.16/0.45 % Level of proof is 3.
% 0.16/0.45 % Maximum clause weight is 21.000.
% 0.16/0.45 % Given clauses 13.
% 0.16/0.45
% 0.16/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------