%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU118+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 : n001.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 25.24s 4.23s
% Output : Proof 25.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 12 unt; 0 def)
% Number of atoms : 107 ( 6 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 116 ( 45 ~; 41 |; 19 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 1 sgn 34 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,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(f6_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)],[f6]) ).
fof(f6_sk,plain,
! [B,A,C] :
( ( ( ( finite(sk0(A,B))
& subset(sk0(A,B),A)
& ~ in(sk0(A,B),B) )
| ( ( ~ finite(sk0(A,B))
| ~ subset(sk0(A,B),A) )
& in(sk0(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,[sk0])],[f6_nnf]) ).
cnf(c9,plain,
( ~ finite(X2)
| ~ subset(X2,X0)
| in(X2,X1)
| X1 != finite_subsets(X0)
| ~ preboolean(X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p91,plain,
( ~ finite(X1)
| ~ subset(X1,X0)
| in(X1,finite_subsets(X0))
| ~ preboolean(finite_subsets(X0)) ),
inference(equality_resolution,[status(thm)],[c9]) ).
fof(f7,axiom,
! [A] : preboolean(finite_subsets(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(f7_nnf,plain,
! [A] : preboolean(finite_subsets(A)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A] : preboolean(finite_subsets(A)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c16,plain,
preboolean(finite_subsets(X0)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p248,plain,
( ~ finite(X0)
| ~ subset(X0,X1)
| in(X0,finite_subsets(X1)) ),
inference(resolution,[status(thm)],[p91,c16]) ).
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(c64,plain,
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
fof(f26,conjecture,
! [A,B] :
( element(B,powerset(A))
=> ( finite(A)
=> element(B,finite_subsets(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_finsub_1) ).
fof(f26_neg,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ( finite(A)
=> element(B,finite_subsets(A)) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f26_nnf,plain,
? [A,B] :
( ~ element(B,finite_subsets(A))
& finite(A)
& element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f26_neg]) ).
fof(f26_sk,plain,
( ~ element(sk12,finite_subsets(sk11))
& finite(sk11)
& element(sk12,powerset(sk11)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11,sk12])],[f26_nnf]) ).
cnf(c61,plain,
element(sk12,powerset(sk11)),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p134,plain,
subset(sk12,sk11),
inference(resolution,[status(thm)],[c64,c61]) ).
cnf(p310,plain,
( ~ finite(sk12)
| in(sk12,finite_subsets(sk11)) ),
inference(resolution,[status(thm)],[p248,p134]) ).
fof(f3,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
fof(f3_nnf,plain,
! [A] :
( ! [B] :
( finite(B)
| ~ element(B,powerset(A)) )
| ~ finite(A) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( finite(B)
| ~ element(B,powerset(A))
| ~ finite(A) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c4,plain,
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(c62,plain,
finite(sk11),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p75,plain,
( finite(X0)
| ~ element(X0,powerset(sk11)) ),
inference(resolution,[status(thm)],[c4,c62]) ).
cnf(p120,plain,
finite(sk12),
inference(resolution,[status(thm)],[p75,c61]) ).
cnf(p393,plain,
in(sk12,finite_subsets(sk11)),
inference(resolution,[status(thm)],[p310,p120]) ).
fof(f24,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f24_nnf,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c59,plain,
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p395,plain,
element(sk12,finite_subsets(sk11)),
inference(resolution,[status(thm)],[p393,c59]) ).
cnf(c63,plain,
~ element(sk12,finite_subsets(sk11)),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p397,plain,
$false,
inference(resolution,[status(thm)],[p395,c63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU118+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 12:53:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 25.24/4.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.24/4.23 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------