%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET873+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 14 unt; 0 def)
% Number of atoms : 34 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 4 |; 2 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 1 sgn 13 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(l21_zfmisc_1,axiom,
! [A,B] :
( subset(set_union2(singleton(A),B),B)
=> in(A,B) ),
file('theBenchmark.p',l21_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t13_zfmisc_1,conjecture,
! [A,B] :
( set_union2(singleton(A),singleton(B)) = singleton(A)
=> A = B ),
file('theBenchmark.p',t13_zfmisc_1) ).
fof(t13_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( set_union2(singleton(A),singleton(B)) = singleton(A)
=> A = B ),
inference(assume_negation,[status(cth)],[t13_zfmisc_1]) ).
cnf(c_13,plain,
set_union2(A,B) = set_union2(B,A),
inference(clausify,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_14,plain,
( C = A
| ~ in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_21,plain,
( in(A,B)
| ~ subset(set_union2(singleton(A),B),B) ),
inference(clausify,[status(thm)],[l21_zfmisc_1]) ).
cnf(c_24,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
fof(nnf_11,plain,
? [A,B] :
( B != A
& singleton(A) = set_union2(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t13_zfmisc_1_neg]) ).
fof(sk_t13_zfmisc_1_neg,plain,
( sK1 != sK0
& singleton(sK0) = set_union2(singleton(sK0),singleton(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_11]) ).
cnf(c_25,negated_conjecture,
singleton(sK0) = set_union2(singleton(sK0),singleton(sK1)),
inference(split_conjunct,[status(thm)],[sk_t13_zfmisc_1_neg]) ).
cnf(c_26,negated_conjecture,
set_union2(singleton(sK0),singleton(sK1)) = singleton(sK0),
inference(copy,[status(thm)],[c_25]) ).
cnf(c_27,negated_conjecture,
sK1 != sK0,
inference(split_conjunct,[status(thm)],[sk_t13_zfmisc_1_neg]) ).
cnf(c_55,negated_conjecture,
singleton(sK0) = set_union2(singleton(sK0),singleton(sK1)),
inference(copy,[status(thm)],[c_26]) ).
cnf(c_56,negated_conjecture,
( A = sK0
| ~ in(A,set_union2(singleton(sK0),singleton(sK1))) ),
inference(resolve,[status(thm)],[c_14,c_55]) ).
cnf(c_57,negated_conjecture,
~ in(sK1,set_union2(singleton(sK0),singleton(sK1))),
inference(resolve,[status(thm)],[c_56,c_27]) ).
cnf(c_42,negated_conjecture,
~ in(sK1,singleton(sK0)),
inference(paramod,[status(thm)],[c_26,c_57]) ).
cnf(c_58,plain,
~ subset(set_union2(singleton(sK1),singleton(sK0)),singleton(sK0)),
inference(resolve,[status(thm)],[c_21,c_42]) ).
cnf(c_59,plain,
~ subset(set_union2(singleton(sK0),singleton(sK1)),singleton(sK0)),
inference(paramod,[status(thm)],[c_13,c_58]) ).
cnf(c_60,plain,
~ subset(singleton(sK0),singleton(sK0)),
inference(paramod,[status(thm)],[c_26,c_59]) ).
cnf(c_54,plain,
$false,
inference(resolve,[status(thm)],[c_24,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET873+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n016.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 26 08:28:15 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 420558 was started by sandbox2 on n016,
% 0.10/0.38 % Sat Sep 26 08:28:15 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).
% 0.10/0.40
% 0.10/0.40 % SZS status Theorem for theBenchmark
% 0.10/0.40
% 0.10/0.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.40 % Length of proof is 14.
% 0.10/0.40 % Level of proof is 4.
% 0.10/0.40 % Maximum clause weight is 10.000.
% 0.10/0.40 % Given clauses 20.
% 0.10/0.40
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------