%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU153+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 08:45:12 AM UTC 2026
% Result : Theorem 0.96s 0.54s
% Output : CNFRefutation 0.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 10 unt; 0 def)
% Number of atoms : 35 ( 2 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 30 ( 15 ~; 5 |; 9 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 1 sgn 12 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l2_zfmisc_1,axiom,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('theBenchmark.p',l2_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t3_xboole_0,axiom,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t3_xboole_0) ).
fof(t69_enumset1,axiom,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
fof(l25_zfmisc_1,conjecture,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('theBenchmark.p',l25_zfmisc_1) ).
fof(l25_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
inference(assume_negation,[status(cth)],[l25_zfmisc_1]) ).
cnf(c_133,plain,
( in(A,B)
| ~ subset(singleton(A),B) ),
inference(clausify,[status(thm)],[l2_zfmisc_1]) ).
cnf(c_142,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_163,plain,
( ~ disjoint(B,C)
| ~ in(A,C)
| ~ in(A,B) ),
inference(clausify,[status(thm)],[t3_xboole_0]) ).
cnf(c_176,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[t69_enumset1]) ).
fof(nnf_74,plain,
? [A,B] :
( in(A,B)
& disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[l25_zfmisc_1_neg]) ).
fof(sk_l25_zfmisc_1_neg,plain,
( in(sK0,sK1)
& disjoint(singleton(sK0),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_74]) ).
cnf(c_190,negated_conjecture,
disjoint(singleton(sK0),sK1),
inference(split_conjunct,[status(thm)],[sk_l25_zfmisc_1_neg]) ).
cnf(c_191,negated_conjecture,
disjoint(unordered_pair(sK0,sK0),sK1),
inference(paramod,[status(thm)],[c_176,c_190]) ).
cnf(c_192,negated_conjecture,
in(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_l25_zfmisc_1_neg]) ).
cnf(c_234,plain,
( in(A,B)
| ~ subset(unordered_pair(A,A),B) ),
inference(paramod,[status(thm)],[c_176,c_133]) ).
cnf(c_776,plain,
( ~ disjoint(A,sK1)
| ~ in(sK0,A) ),
inference(resolve,[status(thm)],[c_192,c_163]) ).
cnf(c_1352,plain,
in(A,unordered_pair(A,A)),
inference(resolve,[status(thm)],[c_234,c_142]) ).
cnf(c_1479,negated_conjecture,
~ in(sK0,unordered_pair(sK0,sK0)),
inference(resolve,[status(thm)],[c_776,c_191]) ).
cnf(c_1478,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1352,c_1479]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU153+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 08:46:01 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 459196 was started by sandbox on n016,
% 0.10/0.37 % Sat Sep 26 08:46:01 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.39
% 0.15/0.39 % From the command line: assign(max_seconds, 300).
% 0.96/0.54
% 0.96/0.54 % SZS status Theorem for theBenchmark
% 0.96/0.54
% 0.96/0.54 % Proof 1 at 0.08 (+ 0.03) seconds.
% 0.96/0.54 % Length of proof is 16.
% 0.96/0.54 % Level of proof is 4.
% 0.96/0.54 % Maximum clause weight is 18.000.
% 0.96/0.54 % Given clauses 145.
% 0.96/0.54
% 0.96/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------