%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET935+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 08:37:19 AM UTC 2026
% Result : Theorem 1.56s 0.61s
% Output : CNFRefutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 60 ( 25 unt; 0 def)
% Number of atoms : 107 ( 39 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 81 ( 34 ~; 36 |; 3 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 7 sgn 23 !; 2 ?)
% 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(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('theBenchmark.p',d1_zfmisc_1) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(d9_xboole_0,axiom,
! [A,B] :
( inclusion_comparable(A,B)
<=> ( subset(B,A)
| subset(A,B) ) ),
file('theBenchmark.p',d9_xboole_0) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t7_xboole_1,axiom,
! [A,B] : subset(A,set_union2(A,B)),
file('theBenchmark.p',t7_xboole_1) ).
fof(t82_zfmisc_1,conjecture,
! [A,B] :
( set_union2(powerset(A),powerset(B)) = powerset(set_union2(A,B))
=> inclusion_comparable(A,B) ),
file('theBenchmark.p',t82_zfmisc_1) ).
fof(t82_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( set_union2(powerset(A),powerset(B)) = powerset(set_union2(A,B))
=> inclusion_comparable(A,B) ),
inference(assume_negation,[status(cth)],[t82_zfmisc_1]) ).
cnf(c_18,plain,
set_union2(A,B) = set_union2(B,A),
inference(clausify,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_21,plain,
( ~ subset(A,B)
| ~ subset(B,A)
| A = B ),
inference(clausify,[status(thm)],[d10_xboole_0]) ).
cnf(c_22,plain,
( subset(C,A)
| ~ in(C,B)
| powerset(A) != B ),
inference(clausify,[status(thm)],[d1_zfmisc_1]) ).
cnf(c_23,plain,
( ~ subset(C,A)
| in(C,B)
| powerset(A) != B ),
inference(clausify,[status(thm)],[d1_zfmisc_1]) ).
cnf(c_26,plain,
( in(D,B)
| in(D,A)
| ~ in(D,C)
| set_union2(A,B) != C ),
inference(clausify,[status(thm)],[d2_xboole_0]) ).
cnf(c_28,plain,
( ~ in(D,B)
| in(D,C)
| set_union2(A,B) != C ),
inference(clausify,[status(thm)],[d2_xboole_0]) ).
cnf(c_33,plain,
( ~ subset(A,B)
| inclusion_comparable(A,B) ),
inference(clausify,[status(thm)],[d9_xboole_0]) ).
cnf(c_34,plain,
( ~ subset(B,A)
| inclusion_comparable(A,B) ),
inference(clausify,[status(thm)],[d9_xboole_0]) ).
cnf(c_37,plain,
set_union2(A,A) = A,
inference(clausify,[status(thm)],[idempotence_k2_xboole_0]) ).
cnf(c_40,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_43,plain,
subset(A,set_union2(A,B)),
inference(clausify,[status(thm)],[t7_xboole_1]) ).
fof(nnf_16,plain,
? [A,B] :
( ~ inclusion_comparable(A,B)
& powerset(set_union2(A,B)) = set_union2(powerset(A),powerset(B)) ),
inference(fof_nnf,[status(thm)],[t82_zfmisc_1_neg]) ).
fof(sk_t82_zfmisc_1_neg,plain,
( ~ inclusion_comparable(sK0,sK1)
& powerset(set_union2(sK0,sK1)) = set_union2(powerset(sK0),powerset(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_16]) ).
cnf(c_44,negated_conjecture,
powerset(set_union2(sK0,sK1)) = set_union2(powerset(sK0),powerset(sK1)),
inference(split_conjunct,[status(thm)],[sk_t82_zfmisc_1_neg]) ).
cnf(c_45,negated_conjecture,
~ inclusion_comparable(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t82_zfmisc_1_neg]) ).
cnf(c_868,plain,
A = set_union2(A,A),
inference(copy,[status(thm)],[c_37]) ).
cnf(c_869,plain,
( ~ subset(A,B)
| in(A,set_union2(powerset(B),powerset(B))) ),
inference(resolve,[status(thm)],[c_23,c_868]) ).
cnf(c_870,plain,
in(A,set_union2(powerset(A),powerset(A))),
inference(resolve,[status(thm)],[c_869,c_40]) ).
cnf(c_212,plain,
in(A,powerset(A)),
inference(paramod,[status(thm)],[c_37,c_870]) ).
cnf(c_871,plain,
( ~ subset(set_union2(A,B),A)
| A = set_union2(A,B) ),
inference(resolve,[status(thm)],[c_43,c_21]) ).
cnf(c_216,plain,
( ~ subset(set_union2(A,B),A)
| set_union2(A,B) = A ),
inference(copy,[status(thm)],[c_871]) ).
cnf(c_218,plain,
subset(A,set_union2(B,A)),
inference(paramod,[status(thm)],[c_18,c_43]) ).
cnf(c_232,negated_conjecture,
~ subset(sK1,sK0),
inference(resolve,[status(thm)],[c_34,c_45]) ).
cnf(c_233,negated_conjecture,
~ subset(sK0,sK1),
inference(resolve,[status(thm)],[c_33,c_45]) ).
cnf(c_872,plain,
A = set_union2(A,A),
inference(copy,[status(thm)],[c_37]) ).
cnf(c_873,plain,
( subset(A,B)
| ~ in(A,set_union2(powerset(B),powerset(B))) ),
inference(resolve,[status(thm)],[c_22,c_872]) ).
cnf(c_874,plain,
~ in(sK1,set_union2(powerset(sK0),powerset(sK0))),
inference(resolve,[status(thm)],[c_873,c_232]) ).
cnf(c_302,plain,
~ in(sK1,powerset(sK0)),
inference(paramod,[status(thm)],[c_37,c_874]) ).
cnf(c_875,negated_conjecture,
set_union2(powerset(sK0),powerset(sK1)) = powerset(set_union2(sK0,sK1)),
inference(copy,[status(thm)],[c_44]) ).
cnf(c_876,negated_conjecture,
( in(A,powerset(sK1))
| in(A,powerset(sK0))
| ~ in(A,powerset(set_union2(sK0,sK1))) ),
inference(resolve,[status(thm)],[c_26,c_875]) ).
cnf(c_313,negated_conjecture,
( in(set_union2(sK0,sK1),powerset(sK1))
| in(set_union2(sK0,sK1),powerset(sK0)) ),
inference(resolve,[status(thm)],[c_876,c_212]) ).
cnf(c_877,plain,
( ~ subset(set_union2(B,A),A)
| A = set_union2(B,A) ),
inference(resolve,[status(thm)],[c_218,c_21]) ).
cnf(c_320,plain,
( ~ subset(set_union2(A,B),B)
| set_union2(A,B) = B ),
inference(copy,[status(thm)],[c_877]) ).
cnf(c_878,plain,
( ~ in(sK1,B)
| set_union2(A,B) != powerset(sK0) ),
inference(resolve,[status(thm)],[c_28,c_302]) ).
cnf(c_329,plain,
set_union2(A,powerset(sK1)) != powerset(sK0),
inference(resolve,[status(thm)],[c_878,c_212]) ).
cnf(c_393,plain,
( ~ subset(set_union2(B,A),A)
| set_union2(A,B) = A ),
inference(paramod,[status(thm)],[c_18,c_216]) ).
cnf(c_394,plain,
( ~ subset(set_union2(B,A),B)
| set_union2(A,B) = B ),
inference(paramod,[status(thm)],[c_18,c_320]) ).
cnf(c_879,plain,
( subset(A,B)
| ~ in(A,powerset(B)) ),
inference(xxres,[status(thm)],[c_22]) ).
cnf(c_811,plain,
( in(set_union2(sK0,sK1),powerset(sK0))
| subset(set_union2(sK0,sK1),sK1) ),
inference(resolve,[status(thm)],[c_879,c_313]) ).
cnf(c_880,plain,
( set_union2(sK1,sK0) = sK1
| in(set_union2(sK0,sK1),powerset(sK0)) ),
inference(resolve,[status(thm)],[c_811,c_393]) ).
cnf(c_812,plain,
( set_union2(sK0,sK1) = sK1
| in(set_union2(sK0,sK1),powerset(sK0)) ),
inference(paramod,[status(thm)],[c_18,c_880]) ).
cnf(c_881,plain,
( subset(A,B)
| ~ in(A,powerset(B)) ),
inference(xxres,[status(thm)],[c_22]) ).
cnf(c_821,plain,
( set_union2(sK0,sK1) = sK1
| subset(set_union2(sK0,sK1),sK0) ),
inference(resolve,[status(thm)],[c_881,c_812]) ).
cnf(c_882,plain,
( set_union2(sK1,sK0) = sK0
| set_union2(sK0,sK1) = sK1 ),
inference(resolve,[status(thm)],[c_821,c_394]) ).
cnf(c_822,plain,
( set_union2(sK0,sK1) = sK0
| set_union2(sK0,sK1) = sK1 ),
inference(paramod,[status(thm)],[c_18,c_882]) ).
cnf(c_883,plain,
( subset(sK0,sK1)
| set_union2(sK0,sK1) = sK0 ),
inference(paramod,[status(thm)],[c_822,c_43]) ).
cnf(c_842,plain,
set_union2(sK0,sK1) = sK0,
inference(resolve,[status(thm)],[c_233,c_883]) ).
cnf(c_884,negated_conjecture,
powerset(sK0) = set_union2(powerset(sK0),powerset(sK1)),
inference(paramod,[status(thm)],[c_842,c_44]) ).
cnf(c_885,negated_conjecture,
set_union2(powerset(sK0),powerset(sK1)) = powerset(sK0),
inference(copy,[status(thm)],[c_884]) ).
cnf(c_867,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_329,c_885]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET935+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 08:29:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3573441 was started by sandbox on n015,
% 0.10/0.37 % Sat Sep 26 08:29:43 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 1.56/0.61
% 1.56/0.61 % Assigning unary symbol powerset kb_weight 0 and highest precedence (13).
% 1.56/0.61
% 1.56/0.61 % SZS status Theorem for theBenchmark
% 1.56/0.61
% 1.56/0.61 % Proof 1 at 0.14 (+ 0.05) seconds.
% 1.56/0.61 % Length of proof is 39.
% 1.56/0.61 % Level of proof is 9.
% 1.56/0.61 % Maximum clause weight is 25.000.
% 1.56/0.61 % Given clauses 101.
% 1.56/0.61
% 1.56/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------