%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU155+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 08:45:13 AM UTC 2026
% Result : Theorem 42.33s 5.86s
% Output : CNFRefutation 42.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 5 unt; 0 def)
% Number of atoms : 71 ( 5 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 70 ( 26 ~; 27 |; 9 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 26 !; 4 ?)
% 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(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('theBenchmark.p',d4_tarski) ).
fof(l50_zfmisc_1,conjecture,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',l50_zfmisc_1) ).
fof(l50_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
inference(assume_negation,[status(cth)],[l50_zfmisc_1]) ).
cnf(c_93,plain,
( subset(C,A)
| ~ in(C,B)
| powerset(A) != B ),
inference(clausify,[status(thm)],[d1_zfmisc_1]) ).
cnf(c_94,plain,
( ~ subset(C,A)
| in(C,B)
| powerset(A) != B ),
inference(clausify,[status(thm)],[d1_zfmisc_1]) ).
fof(nnf_12,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(sK0(A,B),B)
& in(sK0(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(A,B))],[nnf_12]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ in(sK0(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK0(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_110,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_111,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_120,plain,
( ~ in(D,A)
| ~ in(C,D)
| in(C,B)
| union(A) != B ),
inference(clausify,[status(thm)],[d4_tarski]) ).
fof(nnf_78,plain,
? [A,B] :
( ~ subset(A,union(B))
& in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1_neg]) ).
fof(sk_l50_zfmisc_1_neg,plain,
( ~ subset(sK1,union(sK2))
& in(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2)],[nnf_78]) ).
cnf(c_202,negated_conjecture,
in(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_l50_zfmisc_1_neg]) ).
cnf(c_203,negated_conjecture,
~ subset(sK1,union(sK2)),
inference(split_conjunct,[status(thm)],[sk_l50_zfmisc_1_neg]) ).
cnf(c_257,plain,
( subset(A,B)
| ~ in(A,powerset(B)) ),
inference(xxres,[status(thm)],[c_93]) ).
cnf(c_259,plain,
( ~ subset(A,B)
| in(A,powerset(B)) ),
inference(xxres,[status(thm)],[c_94]) ).
cnf(c_454,plain,
( ~ in(C,B)
| ~ in(A,C)
| in(A,union(B)) ),
inference(xxres,[status(thm)],[c_120]) ).
cnf(c_2033,plain,
( in(sK0(A,B),A)
| in(A,powerset(B)) ),
inference(resolve,[status(thm)],[c_259,c_110]) ).
cnf(c_6626,plain,
( ~ in(A,sK1)
| in(A,union(sK2)) ),
inference(resolve,[status(thm)],[c_454,c_202]) ).
cnf(c_6676,plain,
( in(sK1,powerset(A))
| in(sK0(sK1,A),union(sK2)) ),
inference(resolve,[status(thm)],[c_6626,c_2033]) ).
cnf(c_16693,plain,
( subset(sK1,union(sK2))
| in(sK1,powerset(union(sK2))) ),
inference(resolve,[status(thm)],[c_6676,c_111]) ).
cnf(c_14719,negated_conjecture,
in(sK1,powerset(union(sK2))),
inference(resolve,[status(thm)],[c_203,c_16693]) ).
cnf(c_16694,plain,
subset(sK1,union(sK2)),
inference(resolve,[status(thm)],[c_14719,c_257]) ).
cnf(c_16692,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_203,c_16694]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU155+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n009.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 08:41:30 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 3876000 was started by sandbox2 on n009,
% 0.18/0.44 % Sat Sep 26 08:41:30 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.47
% 0.18/0.47 % From the command line: assign(max_seconds, 300).
% 42.33/5.86
% 42.33/5.86 % given #500 (W,wt=19): 1728 empty_set = A | in(f7(B,empty_set,A),A). [resolve(255,a,236,c),rewrite([172(2),229(1)])].
% 42.33/5.86
% 42.33/5.86 % given #1000 (F,wt=21): 8370 -in(f5(c3,c3,empty_set),A) | -disjoint(set_union2(c3,B),A). [resolve(8228,a,175,a)].
% 42.33/5.86
% 42.33/5.86 % given #1500 (W,wt=17): 14871 -in(union(c4),f5(empty_set,c3,empty_set)). [resolve(14782,a,79,b)].
% 42.33/5.86
% 42.33/5.86 % SZS status Theorem for theBenchmark
% 42.33/5.86
% 42.33/5.86 % Proof 1 at 4.09 (+ 1.21) seconds.
% 42.33/5.86 % Length of proof is 19.
% 42.33/5.86 % Level of proof is 6.
% 42.33/5.86 % Maximum clause weight is 23.000.
% 42.33/5.86 % Given clauses 1881.
% 42.33/5.86
% 42.33/5.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------