%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU113+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 : Fri Sep 25 02:50:58 PM UTC 2026
% Result : Theorem 25.73s 4.22s
% Output : Proof 25.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 12 unt; 0 def)
% Number of atoms : 123 ( 6 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 129 ( 45 ~; 49 |; 28 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 66 ( 2 sgn 38 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B] :
( preboolean(B)
=> ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( finite(C)
& subset(C,A) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_finsub_1) ).
fof(f7_nnf,plain,
! [A,B] :
( ( ( ? [C] :
( ( finite(C)
& subset(C,A)
& ~ in(C,B) )
| ( ( ~ finite(C)
| ~ subset(C,A) )
& in(C,B) ) )
| B = finite_subsets(A) )
& ( ! [C] :
( ( ~ finite(C)
| ~ subset(C,A)
| in(C,B) )
& ( ( finite(C)
& subset(C,A) )
| ~ in(C,B) ) )
| B != finite_subsets(A) ) )
| ~ preboolean(B) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [B,A,C] :
( ( ( ( finite(sk1(A,B))
& subset(sk1(A,B),A)
& ~ in(sk1(A,B),B) )
| ( ( ~ finite(sk1(A,B))
| ~ subset(sk1(A,B),A) )
& in(sk1(A,B),B) )
| B = finite_subsets(A) )
& ( ( ( ~ finite(C)
| ~ subset(C,A)
| in(C,B) )
& ( ( finite(C)
& subset(C,A) )
| ~ in(C,B) ) )
| B != finite_subsets(A) ) )
| ~ preboolean(B) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f7_nnf]) ).
cnf(c10,plain,
( subset(X2,X0)
| ~ in(X2,X1)
| X1 != finite_subsets(X0)
| ~ preboolean(X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p84,plain,
( subset(X1,X0)
| ~ in(X1,finite_subsets(X0))
| ~ preboolean(finite_subsets(X0)) ),
inference(equality_resolution,[status(thm)],[c10]) ).
fof(f8,axiom,
! [A] : preboolean(finite_subsets(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(f8_nnf,plain,
! [A] : preboolean(finite_subsets(A)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A] : preboolean(finite_subsets(A)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c19,plain,
preboolean(finite_subsets(X0)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p175,plain,
( subset(X0,X1)
| ~ in(X0,finite_subsets(X1)) ),
inference(resolution,[status(thm)],[p84,c19]) ).
fof(f6,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f6_nnf,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk0(A,B),B)
& in(sk0(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f6_nnf]) ).
cnf(c8,plain,
( in(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p176,plain,
( subset(finite_subsets(X0),X1)
| subset(sk0(finite_subsets(X0),X1),X0) ),
inference(resolution,[status(thm)],[p175,c8]) ).
fof(f27,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f27_nnf,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c65,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p232,plain,
( element(sk0(finite_subsets(X0),X1),powerset(X0))
| subset(finite_subsets(X0),X1) ),
inference(resolution,[status(thm)],[p176,c65]) ).
fof(f26,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f26_nnf,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c63,plain,
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p444,plain,
( in(sk0(finite_subsets(X0),X1),powerset(X0))
| empty(powerset(X0))
| subset(finite_subsets(X0),X1) ),
inference(resolution,[status(thm)],[p232,c63]) ).
cnf(c9,plain,
( ~ in(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p2170,plain,
( subset(finite_subsets(X0),powerset(X0))
| empty(powerset(X0))
| subset(finite_subsets(X0),powerset(X0)) ),
inference(resolution,[status(thm)],[p444,c9]) ).
cnf(p2210,plain,
( empty(powerset(X0))
| subset(finite_subsets(X0),powerset(X0)) ),
inference(factoring,[status(thm)],[p2170]) ).
fof(f25,conjecture,
! [A] : subset(finite_subsets(A),powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_finsub_1) ).
fof(f25_neg,negated_conjecture,
~ ! [A] : subset(finite_subsets(A),powerset(A)),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f25_nnf,plain,
? [A] : ~ subset(finite_subsets(A),powerset(A)),
inference(nnf_transformation,[status(thm)],[f25_neg]) ).
fof(f25_sk,plain,
~ subset(finite_subsets(sk12),powerset(sk12)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12])],[f25_nnf]) ).
cnf(c62,plain,
~ subset(finite_subsets(sk12),powerset(sk12)),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p2211,plain,
empty(powerset(sk12)),
inference(resolution,[status(thm)],[p2210,c62]) ).
fof(f10,axiom,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finsub_1) ).
fof(f10_nnf,plain,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c21,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p2216,plain,
$false,
inference(resolution,[status(thm)],[p2211,c21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU113+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n020.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 12:47:33 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 25.73/4.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.73/4.22 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------