%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU160+3 : 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 : n015.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 08:45:14 AM UTC 2026
% Result : Theorem 0.10s 5.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 6 unt; 0 def)
% Number of atoms : 75 ( 50 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 74 ( 27 ~; 38 |; 6 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 16 ( 3 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(l4_zfmisc_1,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',l4_zfmisc_1) ).
fof(t39_zfmisc_1,conjecture,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',t39_zfmisc_1) ).
fof(t39_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
inference(assume_negation,[status(cth)],[t39_zfmisc_1]) ).
cnf(c_6,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_10,plain,
( singleton(B) = A
| empty_set = A
| ~ subset(A,singleton(B)) ),
inference(clausify,[status(thm)],[l4_zfmisc_1]) ).
cnf(c_11,plain,
( empty_set != A
| subset(A,singleton(B)) ),
inference(clausify,[status(thm)],[l4_zfmisc_1]) ).
fof(nnf_5,plain,
? [A,B] :
( ( ( singleton(B) != A
& empty_set != A )
| ~ subset(A,singleton(B)) )
& ( singleton(B) = A
| empty_set = A
| subset(A,singleton(B)) ) ),
inference(fof_nnf,[status(thm)],[t39_zfmisc_1_neg]) ).
fof(sk_t39_zfmisc_1_neg_sk,plain,
( ( ( singleton(sK1) != sK0
& empty_set != sK0 )
| ~ subset(sK0,singleton(sK1)) )
& ( singleton(sK1) = sK0
| empty_set = sK0
| subset(sK0,singleton(sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_5]) ).
fof(sk_t39_zfmisc_1_neg,plain,
( ( singleton(sK1) != sK0
| ~ subset(sK0,singleton(sK1)) )
& ( empty_set != sK0
| ~ subset(sK0,singleton(sK1)) )
& ( singleton(sK1) = sK0
| empty_set = sK0
| subset(sK0,singleton(sK1)) ) ),
inference(cnf_transformation,[status(thm)],[sk_t39_zfmisc_1_neg_sk]) ).
cnf(c_13,negated_conjecture,
( singleton(sK1) = sK0
| empty_set = sK0
| subset(sK0,singleton(sK1)) ),
inference(split_conjunct,[status(thm)],[sk_t39_zfmisc_1_neg]) ).
cnf(c_14,negated_conjecture,
( singleton(sK1) = sK0
| sK0 = empty_set
| subset(sK0,singleton(sK1)) ),
inference(copy,[status(thm)],[c_13]) ).
cnf(c_15,negated_conjecture,
( empty_set != sK0
| ~ subset(sK0,singleton(sK1)) ),
inference(split_conjunct,[status(thm)],[sk_t39_zfmisc_1_neg]) ).
cnf(c_16,negated_conjecture,
( sK0 != empty_set
| ~ subset(sK0,singleton(sK1)) ),
inference(copy,[status(thm)],[c_15]) ).
cnf(c_17,negated_conjecture,
( singleton(sK1) != sK0
| ~ subset(sK0,singleton(sK1)) ),
inference(split_conjunct,[status(thm)],[sk_t39_zfmisc_1_neg]) ).
cnf(c_18,plain,
subset(empty_set,singleton(A)),
inference(xxres,[status(thm)],[c_11]) ).
cnf(c_28,negated_conjecture,
( singleton(sK1) = sK0
| empty_set = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_14,c_10]) ).
cnf(c_29,negated_conjecture,
( singleton(sK1) = sK0
| sK0 = empty_set
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_28]) ).
cnf(c_30,negated_conjecture,
( singleton(sK1) = sK0
| singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_29]) ).
cnf(c_19,negated_conjecture,
( singleton(sK1) = sK0
| sK0 = empty_set ),
inference(copy,[status(thm)],[c_30]) ).
cnf(c_31,plain,
( singleton(sK1) != sK0
| ~ subset(sK0,sK0)
| sK0 = empty_set ),
inference(paramod,[status(thm)],[c_19,c_17]) ).
cnf(c_23,plain,
( singleton(sK1) != sK0
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_6,c_31]) ).
cnf(c_32,plain,
( sK0 = empty_set
| sK0 = empty_set ),
inference(resolve,[status(thm)],[c_23,c_19]) ).
cnf(c_25,plain,
sK0 = empty_set,
inference(copy,[status(thm)],[c_32]) ).
cnf(c_33,negated_conjecture,
( sK0 != empty_set
| ~ subset(empty_set,singleton(sK1)) ),
inference(paramod,[status(thm)],[c_25,c_16]) ).
cnf(c_34,negated_conjecture,
( empty_set != empty_set
| ~ subset(empty_set,singleton(sK1)) ),
inference(paramod,[status(thm)],[c_25,c_33]) ).
cnf(c_35,negated_conjecture,
~ subset(empty_set,singleton(sK1)),
inference(copy,[status(thm)],[c_34]) ).
cnf(c_27,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_18,c_35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU160+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n015.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 26 08:45:34 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.37 % Process 3615740 was started by sandbox2 on n015,
% 0.10/5.37 % Sat Sep 26 08:45:34 2026
% 0.10/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.38
% 0.10/5.38 % From the command line: assign(max_seconds, 300).
% 0.10/5.39
% 0.10/5.39 % SZS status Theorem for theBenchmark
% 0.10/5.39
% 0.10/5.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/5.39 % Length of proof is 16.
% 0.10/5.39 % Level of proof is 6.
% 0.10/5.39 % Maximum clause weight is 11.000.
% 0.10/5.39 % Given clauses 15.
% 0.10/5.39
% 0.10/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------