%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU147+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 08:45:10 AM UTC 2026
% Result : Theorem 207.30s 27.71s
% Output : CNFRefutation 207.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 16 unt; 0 def)
% Number of atoms : 119 ( 79 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 121 ( 40 ~; 61 |; 15 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 77 ( 2 sgn 42 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
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_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
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(t3_xboole_1,axiom,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('theBenchmark.p',t3_xboole_1) ).
fof(t69_enumset1,axiom,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
fof(t1_zfmisc_1,conjecture,
powerset(empty_set) = singleton(empty_set),
file('theBenchmark.p',t1_zfmisc_1) ).
fof(t1_zfmisc_1_neg,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(assume_negation,[status(cth)],[t1_zfmisc_1]) ).
cnf(c_84,plain,
( subset(C,A)
| ~ in(C,B)
| powerset(A) != B ),
inference(clausify,[status(thm)],[d1_zfmisc_1]) ).
cnf(c_85,plain,
( ~ subset(C,A)
| in(C,B)
| powerset(A) != B ),
inference(clausify,[status(thm)],[d1_zfmisc_1]) ).
fof(nnf_10,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( D != B
& D != A )
| ~ in(D,C) )
& ( D = B
| D = A
| in(D,C) ) )
| unordered_pair(A,B) = C )
& ( ! [X0] :
( ( ( X0 != B
& X0 != A )
| in(X0,C) )
& ( X0 = B
| X0 = A
| ~ in(X0,C) ) )
| unordered_pair(A,B) != C ) ),
inference(fof_nnf,[status(thm)],[d2_tarski]) ).
fof(sk_d2_tarski_sk,plain,
! [A,B,C] :
( ( ( ( ( sK0(A,B,C) != B
& sK0(A,B,C) != A )
| ~ in(sK0(A,B,C),C) )
& ( sK0(A,B,C) = B
| sK0(A,B,C) = A
| in(sK0(A,B,C),C) ) )
| unordered_pair(A,B) = C )
& ( ! [X0] :
( ( ( X0 != B
& X0 != A )
| in(X0,C) )
& ( X0 = B
| X0 = A
| ~ in(X0,C) ) )
| unordered_pair(A,B) != C ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(D,sK0(A,B,C))],[nnf_10]) ).
fof(sk_d2_tarski,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( sK0(VAR_0,VAR_1,VAR_2) != VAR_1
| ~ in(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| unordered_pair(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( sK0(VAR_0,VAR_1,VAR_2) != VAR_0
| ~ in(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| unordered_pair(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( sK0(VAR_0,VAR_1,VAR_2) = VAR_1
| sK0(VAR_0,VAR_1,VAR_2) = VAR_0
| in(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| unordered_pair(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 != VAR_1
| in(VAR_3,VAR_2)
| unordered_pair(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 != VAR_0
| in(VAR_3,VAR_2)
| unordered_pair(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = VAR_1
| VAR_3 = VAR_0
| ~ in(VAR_3,VAR_2)
| unordered_pair(VAR_0,VAR_1) != VAR_2 ) ),
inference(cnf_transformation,[status(thm)],[sk_d2_tarski_sk]) ).
cnf(c_91,plain,
( sK0(A,B,C) = B
| sK0(A,B,C) = A
| in(sK0(A,B,C),C)
| unordered_pair(A,B) = C ),
inference(split_conjunct,[status(thm)],[sk_d2_tarski]) ).
cnf(c_93,plain,
( sK0(A,B,C) != B
| ~ in(sK0(A,B,C),C)
| unordered_pair(A,B) = C ),
inference(split_conjunct,[status(thm)],[sk_d2_tarski]) ).
cnf(c_123,plain,
set_union2(A,A) = A,
inference(clausify,[status(thm)],[idempotence_k2_xboole_0]) ).
cnf(c_136,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_156,plain,
( empty_set = A
| ~ subset(A,empty_set) ),
inference(clausify,[status(thm)],[t3_xboole_1]) ).
cnf(c_168,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[t69_enumset1]) ).
cnf(c_176,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(clausify,[status(thm)],[t1_zfmisc_1_neg]) ).
cnf(c_177,negated_conjecture,
powerset(empty_set) != unordered_pair(empty_set,empty_set),
inference(paramod,[status(thm)],[c_168,c_176]) ).
cnf(c_7611,plain,
( subset(A,B)
| ~ in(A,powerset(B)) ),
inference(xxres,[status(thm)],[c_84]) ).
cnf(c_7612,plain,
( sK0(A,B,powerset(C)) = B
| sK0(A,B,powerset(C)) = A
| unordered_pair(A,B) = powerset(C)
| subset(sK0(A,B,powerset(C)),C) ),
inference(resolve,[status(thm)],[c_7611,c_91]) ).
cnf(c_255,plain,
( sK0(A,B,powerset(C)) = B
| sK0(A,B,powerset(C)) = A
| powerset(C) = unordered_pair(A,B)
| subset(sK0(A,B,powerset(C)),C) ),
inference(copy,[status(thm)],[c_7612]) ).
cnf(c_7613,plain,
A = set_union2(A,A),
inference(copy,[status(thm)],[c_123]) ).
cnf(c_7614,plain,
( ~ subset(A,B)
| in(A,set_union2(powerset(B),powerset(B))) ),
inference(resolve,[status(thm)],[c_85,c_7613]) ).
cnf(c_7615,plain,
in(A,set_union2(powerset(A),powerset(A))),
inference(resolve,[status(thm)],[c_7614,c_136]) ).
cnf(c_541,plain,
in(A,powerset(A)),
inference(paramod,[status(thm)],[c_123,c_7615]) ).
cnf(c_7616,plain,
( empty_set = sK0(A,B,powerset(empty_set))
| sK0(A,B,powerset(empty_set)) = B
| sK0(A,B,powerset(empty_set)) = A
| powerset(empty_set) = unordered_pair(A,B) ),
inference(resolve,[status(thm)],[c_255,c_156]) ).
cnf(c_4227,plain,
( sK0(A,B,powerset(empty_set)) = empty_set
| sK0(A,B,powerset(empty_set)) = B
| sK0(A,B,powerset(empty_set)) = A
| powerset(empty_set) = unordered_pair(A,B) ),
inference(copy,[status(thm)],[c_7616]) ).
cnf(c_4245,plain,
( sK0(A,A,powerset(empty_set)) = empty_set
| sK0(A,A,powerset(empty_set)) = A
| powerset(empty_set) = unordered_pair(A,A) ),
inference(factor,[status(thm)],[c_4227]) ).
cnf(c_7617,plain,
( sK0(empty_set,empty_set,powerset(empty_set)) = empty_set
| powerset(empty_set) = unordered_pair(empty_set,empty_set) ),
inference(factor,[status(thm)],[c_4245]) ).
cnf(c_4260,negated_conjecture,
sK0(empty_set,empty_set,powerset(empty_set)) = empty_set,
inference(resolve,[status(thm)],[c_177,c_7617]) ).
cnf(c_7618,plain,
( ~ in(sK0(empty_set,empty_set,powerset(empty_set)),powerset(empty_set))
| unordered_pair(empty_set,empty_set) = powerset(empty_set) ),
inference(resolve,[status(thm)],[c_4260,c_93]) ).
cnf(c_7619,plain,
( ~ in(empty_set,powerset(empty_set))
| unordered_pair(empty_set,empty_set) = powerset(empty_set) ),
inference(paramod,[status(thm)],[c_4260,c_7618]) ).
cnf(c_7620,plain,
( ~ in(empty_set,powerset(empty_set))
| powerset(empty_set) = unordered_pair(empty_set,empty_set) ),
inference(copy,[status(thm)],[c_7619]) ).
cnf(c_7621,negated_conjecture,
~ in(empty_set,powerset(empty_set)),
inference(resolve,[status(thm)],[c_177,c_7620]) ).
cnf(c_7610,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_541,c_7621]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU147+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n013.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 08:39:51 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 2354370 was started by sandbox on n013,
% 0.15/0.43 % Sat Sep 26 08:39:51 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.46
% 0.15/0.46 % From the command line: assign(max_seconds, 300).
% 207.30/27.71
% 207.30/27.71 % SZS status Theorem for theBenchmark
% 207.30/27.71
% 207.30/27.71 % Proof 1 at 2.38 (+ 0.73) seconds.
% 207.30/27.71 % Length of proof is 23.
% 207.30/27.71 % Level of proof is 6.
% 207.30/27.71 % Maximum clause weight is 27.000.
% 207.30/27.71 % Given clauses 307.
% 207.30/27.71
% 207.30/27.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------