%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU114+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 02:50:58 PM UTC 2026
% Result : Theorem 43.72s 6.88s
% Output : Proof 43.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 14 unt; 0 def)
% Number of atoms : 158 ( 20 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 166 ( 62 ~; 66 |; 26 &)
% ( 5 <=>; 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; 1 con; 0-2 aty)
% Number of variables : 85 ( 1 sgn 50 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,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(f8_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)],[f8]) ).
fof(f8_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])],[f8_nnf]) ).
cnf(c15,plain,
( ~ finite(X2)
| ~ subset(X2,X0)
| in(X2,X1)
| X1 != finite_subsets(X0)
| ~ preboolean(X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p119,plain,
( ~ finite(X1)
| ~ subset(X1,X0)
| in(X1,finite_subsets(X0))
| ~ preboolean(finite_subsets(X0)) ),
inference(equality_resolution,[status(thm)],[c15]) ).
fof(f9,axiom,
! [A] : preboolean(finite_subsets(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(f9_nnf,plain,
! [A] : preboolean(finite_subsets(A)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A] : preboolean(finite_subsets(A)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c22,plain,
preboolean(finite_subsets(X0)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p316,plain,
( ~ finite(X0)
| ~ subset(X0,X1)
| in(X0,finite_subsets(X1)) ),
inference(resolution,[status(thm)],[p119,c22]) ).
fof(f26,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f26_nnf,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c65,plain,
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
fof(f7,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f7_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)],[f7]) ).
fof(f7_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])],[f7_nnf]) ).
cnf(c11,plain,
( in(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p117,plain,
( subset(X0,X1)
| element(sk0(X0,X1),X0) ),
inference(resolution,[status(thm)],[c65,c11]) ).
fof(f30,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f30_nnf,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c70,plain,
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(p216,plain,
( subset(sk0(powerset(X0),X1),X0)
| subset(powerset(X0),X1) ),
inference(resolution,[status(thm)],[p117,c70]) ).
cnf(p411,plain,
( subset(powerset(X0),X1)
| ~ finite(sk0(powerset(X0),X1))
| in(sk0(powerset(X0),X1),finite_subsets(X0)) ),
inference(resolution,[status(thm)],[p316,p216]) ).
fof(f3,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('/export/starexec/sandbox/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]) ).
fof(f28,conjecture,
! [A] :
( finite(A)
=> finite_subsets(A) = powerset(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finsub_1) ).
fof(f28_neg,negated_conjecture,
~ ! [A] :
( finite(A)
=> finite_subsets(A) = powerset(A) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f28_nnf,plain,
? [A] :
( finite_subsets(A) != powerset(A)
& finite(A) ),
inference(nnf_transformation,[status(thm)],[f28_neg]) ).
fof(f28_sk,plain,
( finite_subsets(sk12) != powerset(sk12)
& finite(sk12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12])],[f28_nnf]) ).
cnf(c67,plain,
finite(sk12),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p81,plain,
( finite(X0)
| ~ element(X0,powerset(sk12)) ),
inference(resolution,[status(thm)],[c4,c67]) ).
cnf(p214,plain,
( finite(sk0(powerset(sk12),X0))
| subset(powerset(sk12),X0) ),
inference(resolution,[status(thm)],[p117,p81]) ).
cnf(p2669,plain,
( subset(powerset(sk12),X0)
| subset(powerset(sk12),X0)
| in(sk0(powerset(sk12),X0),finite_subsets(sk12)) ),
inference(resolution,[status(thm)],[p411,p214]) ).
cnf(p8119,plain,
( subset(powerset(sk12),X0)
| in(sk0(powerset(sk12),X0),finite_subsets(sk12)) ),
inference(factoring,[status(thm)],[p2669]) ).
cnf(c12,plain,
( ~ in(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p8121,plain,
( subset(powerset(sk12),finite_subsets(sk12))
| subset(powerset(sk12),finite_subsets(sk12)) ),
inference(resolution,[status(thm)],[p8119,c12]) ).
cnf(p8124,plain,
subset(powerset(sk12),finite_subsets(sk12)),
inference(factoring,[status(thm)],[p8121]) ).
fof(f27,axiom,
! [A] : subset(finite_subsets(A),powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finsub_1) ).
fof(f27_nnf,plain,
! [A] : subset(finite_subsets(A),powerset(A)),
inference(nnf_transformation,[status(thm)],[f27]) ).
fof(f27_sk,plain,
! [A] : subset(finite_subsets(A),powerset(A)),
inference(skolemisation,[status(esa)],[f27_nnf]) ).
cnf(c66,plain,
subset(finite_subsets(X0),powerset(X0)),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
fof(f6,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f6_nnf,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c9,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p89,plain,
( ~ subset(powerset(X0),finite_subsets(X0))
| finite_subsets(X0) = powerset(X0) ),
inference(resolution,[status(thm)],[c66,c9]) ).
cnf(p8159,plain,
finite_subsets(sk12) = powerset(sk12),
inference(resolution,[status(thm)],[p8124,p89]) ).
cnf(c68,plain,
finite_subsets(sk12) != powerset(sk12),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p8160,plain,
powerset(sk12) != powerset(sk12),
inference(demodulation,[status(thm)],[p8159,c68]) ).
cnf(p8180,plain,
$false,
inference(equality_resolution,[status(thm)],[p8160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU114+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 12:49:19 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 43.72/6.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.72/6.88 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------