%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET921+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 : n004.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 08:37:17 AM UTC 2026
% Result : Theorem 0.18s 5.66s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 36 ( 6 unt; 0 def)
% Number of atoms : 96 ( 40 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 100 ( 40 ~; 45 |; 9 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 7 sgn 13 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d4_xboole_0) ).
fof(t64_zfmisc_1,conjecture,
! [A,B,C] :
( in(A,set_difference(B,singleton(C)))
<=> ( A != C
& in(A,B) ) ),
file('theBenchmark.p',t64_zfmisc_1) ).
fof(t64_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
( in(A,set_difference(B,singleton(C)))
<=> ( A != C
& in(A,B) ) ),
inference(assume_negation,[status(cth)],[t64_zfmisc_1]) ).
cnf(c_8,plain,
( C = A
| ~ in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_9,plain,
( C != A
| in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_12,plain,
( in(D,A)
| ~ in(D,C)
| set_difference(A,B) != C ),
inference(clausify,[status(thm)],[d4_xboole_0]) ).
cnf(c_13,plain,
( ~ in(D,B)
| ~ in(D,C)
| set_difference(A,B) != C ),
inference(clausify,[status(thm)],[d4_xboole_0]) ).
cnf(c_14,plain,
( in(D,B)
| ~ in(D,A)
| in(D,C)
| set_difference(A,B) != C ),
inference(clausify,[status(thm)],[d4_xboole_0]) ).
fof(nnf_6,plain,
? [A,B,C] :
( ( C = A
| ~ in(A,B)
| ~ in(A,set_difference(B,singleton(C))) )
& ( ( C != A
& in(A,B) )
| in(A,set_difference(B,singleton(C))) ) ),
inference(fof_nnf,[status(thm)],[t64_zfmisc_1_neg]) ).
fof(sk_t64_zfmisc_1_neg_sk,plain,
( ( sK2 = sK0
| ~ in(sK0,sK1)
| ~ in(sK0,set_difference(sK1,singleton(sK2))) )
& ( ( sK2 != sK0
& in(sK0,sK1) )
| in(sK0,set_difference(sK1,singleton(sK2))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_6]) ).
fof(sk_t64_zfmisc_1_neg,plain,
( ( sK2 = sK0
| ~ in(sK0,sK1)
| ~ in(sK0,set_difference(sK1,singleton(sK2))) )
& ( sK2 != sK0
| in(sK0,set_difference(sK1,singleton(sK2))) )
& ( in(sK0,sK1)
| in(sK0,set_difference(sK1,singleton(sK2))) ) ),
inference(cnf_transformation,[status(thm)],[sk_t64_zfmisc_1_neg_sk]) ).
cnf(c_20,negated_conjecture,
( in(sK0,sK1)
| in(sK0,set_difference(sK1,singleton(sK2))) ),
inference(split_conjunct,[status(thm)],[sk_t64_zfmisc_1_neg]) ).
cnf(c_21,negated_conjecture,
( sK2 != sK0
| in(sK0,set_difference(sK1,singleton(sK2))) ),
inference(split_conjunct,[status(thm)],[sk_t64_zfmisc_1_neg]) ).
cnf(c_22,negated_conjecture,
( sK2 = sK0
| ~ in(sK0,sK1)
| ~ in(sK0,set_difference(sK1,singleton(sK2))) ),
inference(split_conjunct,[status(thm)],[sk_t64_zfmisc_1_neg]) ).
cnf(c_29,plain,
( A != B
| in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_9]) ).
cnf(c_394,negated_conjecture,
( in(sK0,A)
| set_difference(A,B) != set_difference(sK1,singleton(sK2))
| in(sK0,sK1) ),
inference(resolve,[status(thm)],[c_20,c_12]) ).
cnf(c_64,negated_conjecture,
( in(sK0,A)
| set_difference(sK1,singleton(sK2)) != set_difference(A,B)
| in(sK0,sK1) ),
inference(copy,[status(thm)],[c_394]) ).
cnf(c_395,plain,
( set_difference(sK1,singleton(sK2)) != set_difference(sK1,A)
| in(sK0,sK1) ),
inference(factor,[status(thm)],[c_64]) ).
cnf(c_70,plain,
in(sK0,sK1),
inference(copy,[status(thm)],[c_395]) ).
cnf(c_71,negated_conjecture,
( sK2 = sK0
| ~ in(sK0,set_difference(sK1,singleton(sK2))) ),
inference(resolve,[status(thm)],[c_70,c_22]) ).
cnf(c_86,plain,
in(A,singleton(A)),
inference(xxres,[status(thm)],[c_29]) ).
cnf(c_95,plain,
( in(sK0,A)
| in(sK0,B)
| set_difference(sK1,A) != B ),
inference(resolve,[status(thm)],[c_70,c_14]) ).
cnf(c_396,plain,
( ~ in(A,C)
| ~ in(A,set_difference(B,C)) ),
inference(xxres,[status(thm)],[c_13]) ).
cnf(c_133,plain,
~ in(A,set_difference(B,singleton(A))),
inference(resolve,[status(thm)],[c_396,c_86]) ).
cnf(c_289,plain,
( in(sK0,A)
| in(sK0,set_difference(sK1,A)) ),
inference(xxres,[status(thm)],[c_95]) ).
cnf(c_290,plain,
( sK2 = sK0
| in(sK0,singleton(sK2)) ),
inference(resolve,[status(thm)],[c_289,c_71]) ).
cnf(c_397,plain,
( sK0 = A
| singleton(A) != singleton(sK2)
| sK2 = sK0 ),
inference(resolve,[status(thm)],[c_290,c_8]) ).
cnf(c_308,plain,
( sK0 = A
| singleton(sK2) != singleton(A)
| sK2 = sK0 ),
inference(copy,[status(thm)],[c_397]) ).
cnf(c_398,plain,
( sK0 = sK2
| sK2 = sK0 ),
inference(xxres,[status(thm)],[c_308]) ).
cnf(c_399,plain,
( sK2 = sK0
| sK2 = sK0 ),
inference(copy,[status(thm)],[c_398]) ).
cnf(c_392,plain,
sK2 = sK0,
inference(copy,[status(thm)],[c_399]) ).
cnf(c_400,negated_conjecture,
( sK2 != sK0
| in(sK0,set_difference(sK1,singleton(sK0))) ),
inference(paramod,[status(thm)],[c_392,c_21]) ).
cnf(c_401,negated_conjecture,
( sK0 != sK0
| in(sK0,set_difference(sK1,singleton(sK0))) ),
inference(paramod,[status(thm)],[c_392,c_400]) ).
cnf(c_402,negated_conjecture,
in(sK0,set_difference(sK1,singleton(sK0))),
inference(copy,[status(thm)],[c_401]) ).
cnf(c_393,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_133,c_402]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET921+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.56 % Computer : n004.cluster.edu
% 0.12/5.56 % Model : x86_64 x86_64
% 0.12/5.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.56 % Memory : 8046.5625MB
% 0.12/5.56 % OS : Linux 6.8.0-71-generic
% 0.12/5.56 % CPULimit : 300
% 0.12/5.56 % WCLimit : 300
% 0.12/5.56 % DateTime : Sat Sep 26 08:25:43 UTC 2026
% 0.12/5.56 % CPUTime :
% 0.12/5.56 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/5.56 % Process 1236628 was started by sandbox2 on n004,
% 0.12/5.56 % Sat Sep 26 08:25:43 2026
% 0.12/5.56 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/5.57
% 0.12/5.57 % From the command line: assign(max_seconds, 300).
% 0.18/5.66
% 0.18/5.66 % SZS status Theorem for theBenchmark
% 0.18/5.66
% 0.18/5.66 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.18/5.66 % Length of proof is 23.
% 0.18/5.66 % Level of proof is 9.
% 0.18/5.66 % Maximum clause weight is 14.000.
% 0.18/5.66 % Given clauses 81.
% 0.18/5.66
% 0.18/5.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------