%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU162+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 08:45:15 AM UTC 2026
% Result : Theorem 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 6 unt; 0 def)
% Number of atoms : 48 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 19 ~; 15 |; 3 &)
% ( 3 <=>; 2 =>; 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 ( 0 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l25_zfmisc_1,axiom,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('theBenchmark.p',l25_zfmisc_1) ).
fof(l28_zfmisc_1,axiom,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('theBenchmark.p',l28_zfmisc_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t83_xboole_1,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('theBenchmark.p',t83_xboole_1) ).
fof(t65_zfmisc_1,conjecture,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('theBenchmark.p',t65_zfmisc_1) ).
fof(t65_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
inference(assume_negation,[status(cth)],[t65_zfmisc_1]) ).
cnf(c_10,plain,
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(clausify,[status(thm)],[l25_zfmisc_1]) ).
cnf(c_11,plain,
( disjoint(singleton(A),B)
| in(A,B) ),
inference(clausify,[status(thm)],[l28_zfmisc_1]) ).
cnf(c_12,plain,
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[symmetry_r1_xboole_0]) ).
cnf(c_13,plain,
( set_difference(A,B) = A
| ~ disjoint(A,B) ),
inference(clausify,[status(thm)],[t83_xboole_1]) ).
cnf(c_14,plain,
( set_difference(A,B) != A
| disjoint(A,B) ),
inference(clausify,[status(thm)],[t83_xboole_1]) ).
fof(nnf_8,plain,
? [A,B] :
( ( in(B,A)
| set_difference(A,singleton(B)) != A )
& ( ~ in(B,A)
| set_difference(A,singleton(B)) = A ) ),
inference(fof_nnf,[status(thm)],[t65_zfmisc_1_neg]) ).
fof(sk_t65_zfmisc_1_neg,plain,
( ( in(sK1,sK0)
| set_difference(sK0,singleton(sK1)) != sK0 )
& ( ~ in(sK1,sK0)
| set_difference(sK0,singleton(sK1)) = sK0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_8]) ).
cnf(c_15,negated_conjecture,
( ~ in(sK1,sK0)
| set_difference(sK0,singleton(sK1)) = sK0 ),
inference(split_conjunct,[status(thm)],[sk_t65_zfmisc_1_neg]) ).
cnf(c_16,negated_conjecture,
( in(sK1,sK0)
| set_difference(sK0,singleton(sK1)) != sK0 ),
inference(split_conjunct,[status(thm)],[sk_t65_zfmisc_1_neg]) ).
cnf(c_19,plain,
( disjoint(singleton(sK1),sK0)
| set_difference(sK0,singleton(sK1)) = sK0 ),
inference(resolve,[status(thm)],[c_15,c_11]) ).
cnf(c_27,plain,
( disjoint(sK0,singleton(sK1))
| set_difference(sK0,singleton(sK1)) = sK0 ),
inference(resolve,[status(thm)],[c_19,c_12]) ).
cnf(c_46,plain,
( set_difference(sK0,singleton(sK1)) = sK0
| set_difference(sK0,singleton(sK1)) = sK0 ),
inference(resolve,[status(thm)],[c_27,c_13]) ).
cnf(c_33,plain,
set_difference(sK0,singleton(sK1)) = sK0,
inference(copy,[status(thm)],[c_46]) ).
cnf(c_47,negated_conjecture,
( in(sK1,sK0)
| sK0 != sK0 ),
inference(paramod,[status(thm)],[c_33,c_16]) ).
cnf(c_34,negated_conjecture,
in(sK1,sK0),
inference(copy,[status(thm)],[c_47]) ).
cnf(c_37,plain,
~ disjoint(singleton(sK1),sK0),
inference(resolve,[status(thm)],[c_34,c_10]) ).
cnf(c_42,plain,
disjoint(sK0,singleton(sK1)),
inference(resolve,[status(thm)],[c_33,c_14]) ).
cnf(c_48,plain,
~ disjoint(sK0,singleton(sK1)),
inference(resolve,[status(thm)],[c_12,c_37]) ).
cnf(c_45,plain,
$false,
inference(resolve,[status(thm)],[c_42,c_48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU162+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 08:45:22 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 1291315 was started by sandbox2 on n002,
% 0.11/0.37 % Sat Sep 26 08:45:22 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.39
% 0.11/0.39 % SZS status Theorem for theBenchmark
% 0.11/0.39
% 0.11/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.39 % Length of proof is 19.
% 0.11/0.39 % Level of proof is 7.
% 0.11/0.39 % Maximum clause weight is 10.000.
% 0.11/0.39 % Given clauses 28.
% 0.11/0.39
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------