%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET987+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 : n008.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 08:37:25 AM UTC 2026
% Result : Theorem 0.18s 10.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 7 unt; 0 def)
% Number of atoms : 19 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 11 ~; 1 |; 2 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t40_xboole_1,axiom,
! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B),
file('theBenchmark.p',t40_xboole_1) ).
fof(t65_zfmisc_1,axiom,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('theBenchmark.p',t65_zfmisc_1) ).
fof(t141_zfmisc_1,conjecture,
! [A,B] :
( ~ in(A,B)
=> set_difference(set_union2(B,singleton(A)),singleton(A)) = B ),
file('theBenchmark.p',t141_zfmisc_1) ).
fof(t141_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( ~ in(A,B)
=> set_difference(set_union2(B,singleton(A)),singleton(A)) = B ),
inference(assume_negation,[status(cth)],[t141_zfmisc_1]) ).
cnf(c_18,plain,
set_difference(set_union2(A,B),B) = set_difference(A,B),
inference(clausify,[status(thm)],[t40_xboole_1]) ).
cnf(c_20,plain,
( in(B,A)
| set_difference(A,singleton(B)) = A ),
inference(clausify,[status(thm)],[t65_zfmisc_1]) ).
fof(nnf_10,plain,
? [A,B] :
( set_difference(set_union2(B,singleton(A)),singleton(A)) != B
& ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t141_zfmisc_1_neg]) ).
fof(sk_t141_zfmisc_1_neg,plain,
( set_difference(set_union2(sK1,singleton(sK0)),singleton(sK0)) != sK1
& ~ in(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_10]) ).
cnf(c_21,negated_conjecture,
~ in(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t141_zfmisc_1_neg]) ).
cnf(c_22,negated_conjecture,
set_difference(set_union2(sK1,singleton(sK0)),singleton(sK0)) != sK1,
inference(split_conjunct,[status(thm)],[sk_t141_zfmisc_1_neg]) ).
cnf(c_23,negated_conjecture,
set_difference(sK1,singleton(sK0)) != sK1,
inference(paramod,[status(thm)],[c_18,c_22]) ).
cnf(c_30,negated_conjecture,
set_difference(sK1,singleton(sK0)) = sK1,
inference(resolve,[status(thm)],[c_21,c_20]) ).
cnf(c_29,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_23,c_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET987+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/10.44 % Computer : n008.cluster.edu
% 0.18/10.44 % Model : x86_64 x86_64
% 0.18/10.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/10.44 % Memory : 8046.5625MB
% 0.18/10.44 % OS : Linux 6.8.0-71-generic
% 0.18/10.44 % CPULimit : 300
% 0.18/10.44 % WCLimit : 300
% 0.18/10.44 % DateTime : Sat Sep 26 08:30:06 UTC 2026
% 0.18/10.45 % CPUTime :
% 0.18/10.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/10.45 % Process 3208960 was started by sandbox2 on n008,
% 0.18/10.45 % Sat Sep 26 08:30:06 2026
% 0.18/10.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/10.45
% 0.18/10.45 % From the command line: assign(max_seconds, 300).
% 0.18/10.47
% 0.18/10.47 % SZS status Theorem for theBenchmark
% 0.18/10.47
% 0.18/10.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/10.47 % Length of proof is 9.
% 0.18/10.47 % Level of proof is 3.
% 0.18/10.47 % Maximum clause weight is 9.000.
% 0.18/10.47 % Given clauses 11.
% 0.18/10.47
% 0.18/10.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------