%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET877+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 08:37:12 AM UTC 2026
% Result : Theorem 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 15 unt; 0 def)
% Number of atoms : 37 ( 28 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 15 ~; 5 |; 2 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 28 ( 1 sgn 13 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(l30_zfmisc_1,axiom,
! [A,B] :
( set_intersection2(A,singleton(B)) = singleton(B)
=> in(B,A) ),
file('theBenchmark.p',l30_zfmisc_1) ).
fof(t18_zfmisc_1,conjecture,
! [A,B] :
( set_intersection2(singleton(A),singleton(B)) = singleton(A)
=> A = B ),
file('theBenchmark.p',t18_zfmisc_1) ).
fof(t18_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( set_intersection2(singleton(A),singleton(B)) = singleton(A)
=> A = B ),
inference(assume_negation,[status(cth)],[t18_zfmisc_1]) ).
cnf(c_10,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(clausify,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_11,plain,
( C = A
| ~ in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_15,plain,
set_intersection2(A,A) = A,
inference(clausify,[status(thm)],[idempotence_k3_xboole_0]) ).
cnf(c_16,plain,
( in(A,B)
| singleton(A) != set_intersection2(B,singleton(A)) ),
inference(clausify,[status(thm)],[l30_zfmisc_1]) ).
cnf(c_17,plain,
( in(B,A)
| set_intersection2(A,singleton(B)) != singleton(B) ),
inference(copy,[status(thm)],[c_16]) ).
fof(nnf_8,plain,
? [A,B] :
( B != A
& singleton(A) = set_intersection2(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t18_zfmisc_1_neg]) ).
fof(sk_t18_zfmisc_1_neg,plain,
( sK1 != sK0
& singleton(sK0) = set_intersection2(singleton(sK0),singleton(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_8]) ).
cnf(c_20,negated_conjecture,
singleton(sK0) = set_intersection2(singleton(sK0),singleton(sK1)),
inference(split_conjunct,[status(thm)],[sk_t18_zfmisc_1_neg]) ).
cnf(c_21,negated_conjecture,
set_intersection2(singleton(sK0),singleton(sK1)) = singleton(sK0),
inference(copy,[status(thm)],[c_20]) ).
cnf(c_22,negated_conjecture,
sK1 != sK0,
inference(split_conjunct,[status(thm)],[sk_t18_zfmisc_1_neg]) ).
cnf(c_43,plain,
A = set_intersection2(A,A),
inference(copy,[status(thm)],[c_15]) ).
cnf(c_44,plain,
( A = B
| ~ in(A,set_intersection2(singleton(B),singleton(B))) ),
inference(resolve,[status(thm)],[c_11,c_43]) ).
cnf(c_45,negated_conjecture,
sK0 != sK1,
inference(copy,[status(thm)],[c_22]) ).
cnf(c_46,negated_conjecture,
~ in(sK0,set_intersection2(singleton(sK1),singleton(sK1))),
inference(resolve,[status(thm)],[c_44,c_45]) ).
cnf(c_35,negated_conjecture,
~ in(sK0,singleton(sK1)),
inference(paramod,[status(thm)],[c_15,c_46]) ).
cnf(c_47,plain,
set_intersection2(singleton(sK1),singleton(sK0)) != singleton(sK0),
inference(resolve,[status(thm)],[c_17,c_35]) ).
cnf(c_48,plain,
set_intersection2(singleton(sK0),singleton(sK1)) != singleton(sK0),
inference(paramod,[status(thm)],[c_10,c_47]) ).
cnf(c_49,plain,
singleton(sK0) != singleton(sK0),
inference(paramod,[status(thm)],[c_21,c_48]) ).
cnf(c_42,plain,
$false,
inference(copy,[status(thm)],[c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET877+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.36 % Computer : n009.cluster.edu
% 0.06/0.36 % Model : x86_64 x86_64
% 0.06/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.36 % Memory : 8046.5625MB
% 0.06/0.36 % OS : Linux 6.8.0-71-generic
% 0.06/0.36 % CPULimit : 300
% 0.06/0.36 % WCLimit : 300
% 0.06/0.36 % DateTime : Sat Sep 26 08:23:44 UTC 2026
% 0.06/0.36 % CPUTime :
% 0.06/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.06/0.36 % Process 3831492 was started by sandbox on n009,
% 0.06/0.36 % Sat Sep 26 08:23:44 2026
% 0.06/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.06/0.37
% 0.06/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.41
% 0.09/0.41 % Assigning unary symbol singleton kb_weight 0 and highest precedence (10).
% 0.09/0.41
% 0.09/0.41 % SZS status Theorem for theBenchmark
% 0.09/0.41
% 0.09/0.41 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.41 % Length of proof is 15.
% 0.09/0.41 % Level of proof is 3.
% 0.09/0.41 % Maximum clause weight is 25.000.
% 0.09/0.41 % Given clauses 16.
% 0.09/0.41
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------