%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU173+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 08:45:18 AM UTC 2026
% Result : Theorem 41.30s 5.67s
% Output : CNFRefutation 41.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 9 unt; 0 def)
% Number of atoms : 78 ( 5 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 72 ( 25 ~; 26 |; 9 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 55 ( 2 sgn 32 !; 3 ?)
% 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_subset_1,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('theBenchmark.p',d2_subset_1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(l71_subset_1,conjecture,
! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
file('theBenchmark.p',l71_subset_1) ).
fof(l71_subset_1_neg,negated_conjecture,
~ ! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
inference(assume_negation,[status(cth)],[l71_subset_1]) ).
fof(nnf_111,plain,
? [A,B] :
( ~ element(A,powerset(B))
& ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(fof_nnf,[status(thm)],[l71_subset_1_neg]) ).
fof(sk_l71_subset_1_neg,plain,
( ~ element(sK0,powerset(sK1))
& ! [C] :
( in(C,sK1)
| ~ in(C,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_111]) ).
cnf(c_112,negated_conjecture,
~ element(sK0,powerset(sK1)),
inference(split_conjunct,[status(thm)],[sk_l71_subset_1_neg]) ).
cnf(c_113,negated_conjecture,
( in(A,sK1)
| ~ in(A,sK0) ),
inference(split_conjunct,[status(thm)],[sk_l71_subset_1_neg]) ).
cnf(c_227,plain,
set_union2(A,A) = A,
inference(clausify,[status(thm)],[idempotence_k2_xboole_0]) ).
cnf(c_232,plain,
~ empty(powerset(A)),
inference(clausify,[status(thm)],[fc1_subset_1]) ).
fof(nnf_14,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(sk_d3_tarski_sk,plain,
! [A,B] :
( ( ( ~ in(sK2(A,B),B)
& in(sK2(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(C,sK2(A,B))],[nnf_14]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ in(sK2(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK2(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,VAR_1)
| ~ in(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_tarski_sk]) ).
cnf(c_268,plain,
( ~ in(sK2(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_269,plain,
( in(sK2(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_297,plain,
( ~ in(B,A)
| element(B,A)
| empty(A) ),
inference(clausify,[status(thm)],[d2_subset_1]) ).
cnf(c_301,plain,
( ~ subset(C,A)
| in(C,B)
| powerset(A) != B ),
inference(clausify,[status(thm)],[d1_zfmisc_1]) ).
cnf(c_19313,plain,
A = set_union2(A,A),
inference(copy,[status(thm)],[c_227]) ).
cnf(c_19314,plain,
( ~ subset(A,B)
| in(A,set_union2(powerset(B),powerset(B))) ),
inference(resolve,[status(thm)],[c_301,c_19313]) ).
cnf(c_2272,plain,
( ~ subset(A,B)
| in(A,powerset(B)) ),
inference(paramod,[status(thm)],[c_227,c_19314]) ).
cnf(c_5254,plain,
( in(sK2(A,B),A)
| in(A,powerset(B)) ),
inference(resolve,[status(thm)],[c_2272,c_269]) ).
cnf(c_15234,plain,
( in(sK2(sK0,A),sK1)
| in(sK0,powerset(A)) ),
inference(resolve,[status(thm)],[c_5254,c_113]) ).
cnf(c_19274,plain,
( subset(sK0,sK1)
| in(sK0,powerset(sK1)) ),
inference(resolve,[status(thm)],[c_15234,c_268]) ).
cnf(c_19315,plain,
( in(sK0,powerset(sK1))
| in(sK0,powerset(sK1)) ),
inference(resolve,[status(thm)],[c_19274,c_2272]) ).
cnf(c_19286,plain,
in(sK0,powerset(sK1)),
inference(copy,[status(thm)],[c_19315]) ).
cnf(c_19316,plain,
( element(sK0,powerset(sK1))
| empty(powerset(sK1)) ),
inference(resolve,[status(thm)],[c_19286,c_297]) ).
cnf(c_19317,plain,
element(sK0,powerset(sK1)),
inference(resolve,[status(thm)],[c_232,c_19316]) ).
cnf(c_19312,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_112,c_19317]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU173+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.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
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Sat Sep 26 08:44:44 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.37 % Process 3884881 was started by sandbox2 on n009,
% 0.14/0.37 % Sat Sep 26 08:44:44 2026
% 0.14/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.40
% 0.14/0.40 % From the command line: assign(max_seconds, 300).
% 41.30/5.67
% 41.30/5.67 % given #500 (T,wt=17): 6380 empty(A) | -in(A,f23(A,A)). [resolve(4050,b,320,b)].
% 41.30/5.67
% 41.30/5.67 % given #1000 (F,wt=15): 14262 -in(f24(A),powerset(empty_set)). [resolve(14181,a,320,b)].
% 41.30/5.67
% 41.30/5.67 % given #1500 (T,wt=16): 17742 subset(unordered_pair(c3,c4),f24(c4)). [resolve(17722,a,415,b)].
% 41.30/5.67
% 41.30/5.67 % SZS status Theorem for theBenchmark
% 41.30/5.67
% 41.30/5.67 % Proof 1 at 3.90 (+ 1.30) seconds.
% 41.30/5.67 % Length of proof is 20.
% 41.30/5.67 % Level of proof is 7.
% 41.30/5.67 % Maximum clause weight is 20.000.
% 41.30/5.67 % Given clauses 1724.
% 41.30/5.67
% 41.30/5.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------