%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET875+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 : n020.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 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 7 unt; 0 def)
% Number of atoms : 27 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 10 ~; 4 |; 5 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 18 ( 0 sgn 9 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(l25_zfmisc_1,axiom,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('theBenchmark.p',l25_zfmisc_1) ).
fof(t16_zfmisc_1,conjecture,
! [A,B] :
~ ( A = B
& disjoint(singleton(A),singleton(B)) ),
file('theBenchmark.p',t16_zfmisc_1) ).
fof(t16_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
~ ( A = B
& disjoint(singleton(A),singleton(B)) ),
inference(assume_negation,[status(cth)],[t16_zfmisc_1]) ).
cnf(c_10,plain,
( C != A
| in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_13,plain,
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(clausify,[status(thm)],[l25_zfmisc_1]) ).
fof(nnf_7,plain,
? [A,B] :
( B = A
& disjoint(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t16_zfmisc_1_neg]) ).
fof(sk_t16_zfmisc_1_neg,plain,
( sK1 = sK0
& disjoint(singleton(sK0),singleton(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_7]) ).
cnf(c_17,negated_conjecture,
disjoint(singleton(sK0),singleton(sK1)),
inference(split_conjunct,[status(thm)],[sk_t16_zfmisc_1_neg]) ).
cnf(c_18,negated_conjecture,
sK1 = sK0,
inference(split_conjunct,[status(thm)],[sk_t16_zfmisc_1_neg]) ).
cnf(c_21,negated_conjecture,
disjoint(singleton(sK0),singleton(sK0)),
inference(paramod,[status(thm)],[c_18,c_17]) ).
cnf(c_22,plain,
( A != B
| in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_10]) ).
cnf(c_28,plain,
~ in(sK0,singleton(sK0)),
inference(resolve,[status(thm)],[c_21,c_13]) ).
cnf(c_30,negated_conjecture,
in(sK1,singleton(sK0)),
inference(resolve,[status(thm)],[c_22,c_18]) ).
cnf(c_31,negated_conjecture,
in(sK0,singleton(sK0)),
inference(paramod,[status(thm)],[c_18,c_30]) ).
cnf(c_29,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_28,c_31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET875+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n020.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 08:24:49 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 1078184 was started by sandbox2 on n020,
% 0.18/0.45 % Sat Sep 26 08:24:49 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 0.18/0.47
% 0.18/0.47 % SZS status Theorem for theBenchmark
% 0.18/0.47
% 0.18/0.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/0.47 % Length of proof is 11.
% 0.18/0.47 % Level of proof is 4.
% 0.18/0.47 % Maximum clause weight is 10.000.
% 0.18/0.47 % Given clauses 13.
% 0.18/0.47
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------