%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU169+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 02:51:12 PM UTC 2026
% Result : Theorem 28.84s 4.83s
% Output : Proof 28.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 10 unt; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 86 ( 32 ~; 28 |; 15 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 1 sgn 30 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f13_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)],[f13]) ).
fof(f13_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk10(A,B),B)
& in(sk10(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f13_nnf]) ).
cnf(c56,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
fof(f9,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f9_nnf,plain,
! [A,B] :
( ( ( ( ~ empty(B)
| element(B,A) )
& ( empty(B)
| ~ element(B,A) ) )
| ~ empty(A) )
& ( ( ( ~ in(B,A)
| element(B,A) )
& ( in(B,A)
| ~ element(B,A) ) )
| empty(A) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B] :
( ( ( ( ~ empty(B)
| element(B,A) )
& ( empty(B)
| ~ element(B,A) ) )
| ~ empty(A) )
& ( ( ( ~ in(B,A)
| element(B,A) )
& ( in(B,A)
| ~ element(B,A) ) )
| empty(A) ) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c22,plain,
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
fof(f46,conjecture,
! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( in(C,B)
=> in(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_subset_1) ).
fof(f46_neg,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ! [C] :
( in(C,B)
=> in(C,A) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f46_nnf,plain,
? [A,B] :
( ? [C] :
( ~ in(C,A)
& in(C,B) )
& element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f46_neg]) ).
fof(f46_sk,plain,
( ~ in(sk19,sk17)
& in(sk19,sk18)
& element(sk18,powerset(sk17)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk17,sk18,sk19])],[f46_nnf]) ).
cnf(c120,plain,
element(sk18,powerset(sk17)),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(p285,plain,
( in(sk18,powerset(sk17))
| empty(powerset(sk17)) ),
inference(resolution,[status(thm)],[c22,c120]) ).
fof(f49,lemma,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).
fof(f49_nnf,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f49]) ).
fof(f49_sk,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f49_nnf]) ).
cnf(c127,plain,
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f49_sk]) ).
cnf(p736,plain,
( subset(sk18,sk17)
| empty(powerset(sk17)) ),
inference(resolution,[status(thm)],[p285,c127]) ).
fof(f32,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f32_nnf,plain,
! [A] : ~ empty(powerset(A)),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [A] : ~ empty(powerset(A)),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c104,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p739,plain,
subset(sk18,sk17),
inference(resolution,[status(thm)],[p736,c104]) ).
cnf(p874,plain,
( in(X0,sk17)
| ~ in(X0,sk18) ),
inference(resolution,[status(thm)],[c56,p739]) ).
cnf(c121,plain,
in(sk19,sk18),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(p880,plain,
in(sk19,sk17),
inference(resolution,[status(thm)],[p874,c121]) ).
cnf(c122,plain,
~ in(sk19,sk17),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(p894,plain,
$false,
inference(resolution,[status(thm)],[p880,c122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU169+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.61 % Computer : n009.cluster.edu
% 0.13/0.61 % Model : x86_64 x86_64
% 0.13/0.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.61 % Memory : 8046.5625MB
% 0.13/0.61 % OS : Linux 6.8.0-71-generic
% 0.13/0.61 % CPULimit : 300
% 0.13/0.61 % WCLimit : 300
% 0.13/0.61 % DateTime : Thu Sep 24 13:01:59 UTC 2026
% 0.13/0.61 % CPUTime :
% 0.13/0.62 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 28.84/4.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 28.84/4.83 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------