%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU110+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 : n018.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 02:50:57 PM UTC 2026
% Result : Theorem 46.51s 12.11s
% Output : Proof 46.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 8 unt; 0 def)
% Number of atoms : 140 ( 7 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 149 ( 56 ~; 63 |; 20 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 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 : 89 ( 2 sgn 46 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,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(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(p88,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/sandbox/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(p179,plain,
( subset(X0,X1)
| ~ in(X0,finite_subsets(X1)) ),
inference(resolution,[status(thm)],[p88,c19]) ).
fof(f6,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/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(p181,plain,
( subset(finite_subsets(X0),X1)
| subset(sk0(finite_subsets(X0),X1),X0) ),
inference(resolution,[status(thm)],[p179,c8]) ).
fof(f25,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f25_nnf,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c62,plain,
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p689,plain,
( subset(sk0(finite_subsets(X0),X1),X2)
| ~ subset(X0,X2)
| subset(finite_subsets(X0),X1) ),
inference(resolution,[status(thm)],[p181,c62]) ).
fof(f26,conjecture,
! [A,B] :
( subset(A,B)
=> subset(finite_subsets(A),finite_subsets(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_finsub_1) ).
fof(f26_neg,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> subset(finite_subsets(A),finite_subsets(B)) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f26_nnf,plain,
? [A,B] :
( ~ subset(finite_subsets(A),finite_subsets(B))
& subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f26_neg]) ).
fof(f26_sk,plain,
( ~ subset(finite_subsets(sk12),finite_subsets(sk13))
& subset(sk12,sk13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12,sk13])],[f26_nnf]) ).
cnf(c63,plain,
subset(sk12,sk13),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p5357,plain,
( subset(sk0(finite_subsets(sk12),X0),sk13)
| subset(finite_subsets(sk12),X0) ),
inference(resolution,[status(thm)],[p689,c63]) ).
cnf(c12,plain,
( ~ finite(X2)
| ~ subset(X2,X0)
| in(X2,X1)
| X1 != finite_subsets(X0)
| ~ preboolean(X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p109,plain,
( ~ finite(X1)
| ~ subset(X1,X0)
| in(X1,finite_subsets(X0))
| ~ preboolean(finite_subsets(X0)) ),
inference(equality_resolution,[status(thm)],[c12]) ).
cnf(p255,plain,
( ~ finite(X0)
| ~ subset(X0,X1)
| in(X0,finite_subsets(X1)) ),
inference(resolution,[status(thm)],[p109,c19]) ).
cnf(p5662,plain,
( ~ finite(sk0(finite_subsets(sk12),X0))
| in(sk0(finite_subsets(sk12),X0),finite_subsets(sk13))
| subset(finite_subsets(sk12),X0) ),
inference(resolution,[status(thm)],[p5357,p255]) ).
fof(f24,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox/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(c61,plain,
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p123,plain,
( subset(X0,X1)
| element(sk0(X0,X1),X0) ),
inference(resolution,[status(thm)],[c61,c8]) ).
fof(f5,axiom,
! [A,B] :
( element(B,finite_subsets(A))
=> finite(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_finsub_1) ).
fof(f5_nnf,plain,
! [A,B] :
( finite(B)
| ~ element(B,finite_subsets(A)) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [B,A] :
( finite(B)
| ~ element(B,finite_subsets(A)) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c6,plain,
( finite(X1)
| ~ element(X1,finite_subsets(X0)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p183,plain,
( finite(sk0(finite_subsets(X0),X1))
| subset(finite_subsets(X0),X1) ),
inference(resolution,[status(thm)],[p123,c6]) ).
cnf(p8248,plain,
( subset(finite_subsets(sk12),X0)
| in(sk0(finite_subsets(sk12),X0),finite_subsets(sk13))
| subset(finite_subsets(sk12),X0) ),
inference(resolution,[status(thm)],[p5662,p183]) ).
cnf(p8249,plain,
( in(sk0(finite_subsets(sk12),X0),finite_subsets(sk13))
| subset(finite_subsets(sk12),X0) ),
inference(factoring,[status(thm)],[p8248]) ).
cnf(c9,plain,
( ~ in(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p8251,plain,
( subset(finite_subsets(sk12),finite_subsets(sk13))
| subset(finite_subsets(sk12),finite_subsets(sk13)) ),
inference(resolution,[status(thm)],[p8249,c9]) ).
cnf(p8255,plain,
subset(finite_subsets(sk12),finite_subsets(sk13)),
inference(factoring,[status(thm)],[p8251]) ).
cnf(c64,plain,
~ subset(finite_subsets(sk12),finite_subsets(sk13)),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p8270,plain,
$false,
inference(resolution,[status(thm)],[p8255,c64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU110+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.38 % Computer : n018.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 12:48:23 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 46.51/12.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 46.51/12.11 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------