%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU117+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 24.48s 4.53s
% Output : Proof 24.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 9 unt; 0 def)
% Number of atoms : 103 ( 6 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 108 ( 38 ~; 37 |; 26 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 2 sgn 31 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f31,axiom,
! [A,B] :
( preboolean(B)
=> ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( finite(C)
& subset(C,A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_finsub_1) ).
fof(f31_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)],[f31]) ).
fof(f31_sk,plain,
! [B,A,C] :
( ( ( ( finite(sk12(A,B))
& subset(sk12(A,B),A)
& ~ in(sk12(A,B),B) )
| ( ( ~ finite(sk12(A,B))
| ~ subset(sk12(A,B),A) )
& in(sk12(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,[sk12])],[f31_nnf]) ).
cnf(c60,plain,
( subset(X2,X0)
| ~ in(X2,X1)
| X1 != finite_subsets(X0)
| ~ preboolean(X1) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p125,plain,
( subset(X1,X0)
| ~ in(X1,finite_subsets(X0))
| ~ preboolean(finite_subsets(X0)) ),
inference(equality_resolution,[status(thm)],[c60]) ).
fof(f10,axiom,
! [A] : preboolean(finite_subsets(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(f10_nnf,plain,
! [A] : preboolean(finite_subsets(A)),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A] : preboolean(finite_subsets(A)),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
preboolean(finite_subsets(X0)),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p220,plain,
( subset(X0,X1)
| ~ in(X0,finite_subsets(X1)) ),
inference(resolution,[status(thm)],[p125,c10]) ).
fof(f30,conjecture,
! [A,B] :
( element(B,finite_subsets(A))
=> element(B,powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_finsub_1) ).
fof(f30_neg,negated_conjecture,
~ ! [A,B] :
( element(B,finite_subsets(A))
=> element(B,powerset(A)) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f30_nnf,plain,
? [A,B] :
( ~ element(B,powerset(A))
& element(B,finite_subsets(A)) ),
inference(nnf_transformation,[status(thm)],[f30_neg]) ).
fof(f30_sk,plain,
( ~ element(sk11,powerset(sk10))
& element(sk11,finite_subsets(sk10)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10,sk11])],[f30_nnf]) ).
cnf(c58,plain,
element(sk11,finite_subsets(sk10)),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
fof(f3,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f3_nnf,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p86,plain,
( in(sk11,finite_subsets(sk10))
| empty(finite_subsets(sk10)) ),
inference(resolution,[status(thm)],[c58,c3]) ).
cnf(p222,plain,
( empty(finite_subsets(sk10))
| subset(sk11,sk10) ),
inference(resolution,[status(thm)],[p220,p86]) ).
fof(f27,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/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(c55,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p223,plain,
( element(sk11,powerset(sk10))
| empty(finite_subsets(sk10)) ),
inference(resolution,[status(thm)],[p222,c55]) ).
cnf(c59,plain,
~ element(sk11,powerset(sk10)),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(p225,plain,
empty(finite_subsets(sk10)),
inference(resolution,[status(thm)],[p223,c59]) ).
fof(f12,axiom,
! [A] :
( preboolean(finite_subsets(A))
& diff_closed(finite_subsets(A))
& cup_closed(finite_subsets(A))
& ~ empty(finite_subsets(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_finsub_1) ).
fof(f12_nnf,plain,
! [A] :
( preboolean(finite_subsets(A))
& diff_closed(finite_subsets(A))
& cup_closed(finite_subsets(A))
& ~ empty(finite_subsets(A)) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A] :
( preboolean(finite_subsets(A))
& diff_closed(finite_subsets(A))
& cup_closed(finite_subsets(A))
& ~ empty(finite_subsets(A)) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c15,plain,
~ empty(finite_subsets(X0)),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p227,plain,
$false,
inference(resolution,[status(thm)],[p225,c15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU117+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:47:03 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 24.48/4.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.48/4.53 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------