%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET902+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 : 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 08:37:15 AM UTC 2026
% Result : Theorem 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 20 unt; 0 def)
% Number of atoms : 82 ( 74 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 78 ( 36 ~; 23 |; 18 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 4 sgn 15 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(l1_zfmisc_1,axiom,
! [A] : singleton(A) != empty_set,
file('theBenchmark.p',l1_zfmisc_1) ).
fof(l4_zfmisc_1,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',l4_zfmisc_1) ).
fof(t7_xboole_1,axiom,
! [A,B] : subset(A,set_union2(A,B)),
file('theBenchmark.p',t7_xboole_1) ).
fof(t43_zfmisc_1,conjecture,
! [A,B,C] :
~ ( ~ ( C = empty_set
& B = singleton(A) )
& ~ ( C = singleton(A)
& B = empty_set )
& ~ ( C = singleton(A)
& B = singleton(A) )
& singleton(A) = set_union2(B,C) ),
file('theBenchmark.p',t43_zfmisc_1) ).
fof(t43_zfmisc_1_neg,negated_conjecture,
~ ! [A,B,C] :
~ ( ~ ( C = empty_set
& B = singleton(A) )
& ~ ( C = singleton(A)
& B = empty_set )
& ~ ( C = singleton(A)
& B = singleton(A) )
& singleton(A) = set_union2(B,C) ),
inference(assume_negation,[status(cth)],[t43_zfmisc_1]) ).
cnf(c_12,plain,
set_union2(A,B) = set_union2(B,A),
inference(clausify,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_16,plain,
set_union2(A,A) = A,
inference(clausify,[status(thm)],[idempotence_k2_xboole_0]) ).
cnf(c_17,plain,
singleton(A) != empty_set,
inference(clausify,[status(thm)],[l1_zfmisc_1]) ).
cnf(c_18,plain,
( singleton(B) = A
| empty_set = A
| ~ subset(A,singleton(B)) ),
inference(clausify,[status(thm)],[l4_zfmisc_1]) ).
cnf(c_24,plain,
subset(A,set_union2(A,B)),
inference(clausify,[status(thm)],[t7_xboole_1]) ).
fof(nnf_11,plain,
? [A,B,C] :
( ( C != empty_set
| singleton(A) != B )
& ( singleton(A) != C
| empty_set != B )
& ( singleton(A) != C
| singleton(A) != B )
& singleton(A) = set_union2(B,C) ),
inference(fof_nnf,[status(thm)],[t43_zfmisc_1_neg]) ).
fof(sk_t43_zfmisc_1_neg,plain,
( ( sK2 != empty_set
| singleton(sK0) != sK1 )
& ( singleton(sK0) != sK2
| empty_set != sK1 )
& ( singleton(sK0) != sK2
| singleton(sK0) != sK1 )
& singleton(sK0) = set_union2(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_11]) ).
cnf(c_25,negated_conjecture,
singleton(sK0) = set_union2(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t43_zfmisc_1_neg]) ).
cnf(c_26,negated_conjecture,
set_union2(sK1,sK2) = singleton(sK0),
inference(copy,[status(thm)],[c_25]) ).
cnf(c_27,negated_conjecture,
( singleton(sK0) != sK2
| singleton(sK0) != sK1 ),
inference(split_conjunct,[status(thm)],[sk_t43_zfmisc_1_neg]) ).
cnf(c_28,negated_conjecture,
( singleton(sK0) != sK2
| empty_set != sK1 ),
inference(split_conjunct,[status(thm)],[sk_t43_zfmisc_1_neg]) ).
cnf(c_29,negated_conjecture,
( singleton(sK0) != sK2
| sK1 != empty_set ),
inference(copy,[status(thm)],[c_28]) ).
cnf(c_30,negated_conjecture,
( sK2 != empty_set
| singleton(sK0) != sK1 ),
inference(split_conjunct,[status(thm)],[sk_t43_zfmisc_1_neg]) ).
cnf(c_34,plain,
subset(A,set_union2(B,A)),
inference(paramod,[status(thm)],[c_12,c_24]) ).
cnf(c_37,plain,
subset(sK1,singleton(sK0)),
inference(paramod,[status(thm)],[c_26,c_24]) ).
cnf(c_87,plain,
( singleton(sK0) = sK1
| empty_set = sK1 ),
inference(resolve,[status(thm)],[c_37,c_18]) ).
cnf(c_46,plain,
( singleton(sK0) = sK1
| sK1 = empty_set ),
inference(copy,[status(thm)],[c_87]) ).
cnf(c_47,plain,
subset(sK2,singleton(sK0)),
inference(paramod,[status(thm)],[c_26,c_34]) ).
cnf(c_88,plain,
( singleton(sK0) = sK2
| empty_set = sK2 ),
inference(resolve,[status(thm)],[c_47,c_18]) ).
cnf(c_48,plain,
( singleton(sK0) = sK2
| sK2 = empty_set ),
inference(copy,[status(thm)],[c_88]) ).
cnf(c_49,plain,
( sK2 != empty_set
| sK1 = empty_set ),
inference(resolve,[status(thm)],[c_46,c_30]) ).
cnf(c_66,plain,
( sK1 != empty_set
| sK2 = empty_set ),
inference(resolve,[status(thm)],[c_48,c_29]) ).
cnf(c_89,negated_conjecture,
( sK1 = empty_set
| singleton(sK0) != sK2 ),
inference(resolve,[status(thm)],[c_27,c_46]) ).
cnf(c_68,negated_conjecture,
( sK2 = empty_set
| sK1 = empty_set ),
inference(resolve,[status(thm)],[c_89,c_48]) ).
cnf(c_90,plain,
( sK1 = empty_set
| sK1 = empty_set ),
inference(resolve,[status(thm)],[c_68,c_49]) ).
cnf(c_84,plain,
sK1 = empty_set,
inference(copy,[status(thm)],[c_90]) ).
cnf(c_91,plain,
( empty_set != empty_set
| sK2 = empty_set ),
inference(paramod,[status(thm)],[c_84,c_66]) ).
cnf(c_85,plain,
sK2 = empty_set,
inference(copy,[status(thm)],[c_91]) ).
cnf(c_92,negated_conjecture,
set_union2(empty_set,sK2) = singleton(sK0),
inference(paramod,[status(thm)],[c_84,c_26]) ).
cnf(c_93,negated_conjecture,
set_union2(empty_set,empty_set) = singleton(sK0),
inference(paramod,[status(thm)],[c_85,c_92]) ).
cnf(c_94,negated_conjecture,
empty_set = singleton(sK0),
inference(paramod,[status(thm)],[c_16,c_93]) ).
cnf(c_95,negated_conjecture,
singleton(sK0) = empty_set,
inference(copy,[status(thm)],[c_94]) ).
cnf(c_86,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_17,c_95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET902+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n015.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 08:28:14 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 3570434 was started by sandbox2 on n015,
% 0.19/0.45 % Sat Sep 26 08:28:14 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.19/0.48
% 0.19/0.48 % Assigning unary symbol singleton kb_weight 0 and highest precedence (11).
% 0.19/0.48
% 0.19/0.48 % SZS status Theorem for theBenchmark
% 0.19/0.48
% 0.19/0.48 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.19/0.48 % Length of proof is 28.
% 0.19/0.48 % Level of proof is 8.
% 0.19/0.48 % Maximum clause weight is 21.000.
% 0.19/0.48 % Given clauses 45.
% 0.19/0.48
% 0.19/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------