%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU354+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 02:51:49 PM UTC 2026
% Result : Theorem 24.21s 4.01s
% Output : Proof 24.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 10 unt; 0 def)
% Number of atoms : 69 ( 21 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 69 ( 29 ~; 23 |; 10 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 33 ( 2 sgn 21 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [A,B] :
( element(B,A)
=> ( proper_element(B,A)
<=> B != union(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tex_2) ).
fof(f16_nnf,plain,
! [A,B] :
( ( ( B = union(A)
| proper_element(B,A) )
& ( B != union(A)
| ~ proper_element(B,A) ) )
| ~ element(B,A) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [B,A] :
( ( ( B = union(A)
| proper_element(B,A) )
& ( B != union(A)
| ~ proper_element(B,A) ) )
| ~ element(B,A) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c41,plain,
( X1 = union(X0)
| proper_element(X1,X0)
| ~ element(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
fof(f38,conjecture,
! [A,B] :
( element(B,powerset(A))
=> ( proper_element(B,powerset(A))
<=> B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_tex_2) ).
fof(f38_neg,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(A))
=> ( proper_element(B,powerset(A))
<=> B != A ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f38_nnf,plain,
? [A,B] :
( ( ( B != A
& ~ proper_element(B,powerset(A)) )
| ( B = A
& proper_element(B,powerset(A)) ) )
& element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f38_neg]) ).
fof(f38_sk,plain,
( ( ( sk6 != sk5
& ~ proper_element(sk6,powerset(sk5)) )
| ( sk6 = sk5
& proper_element(sk6,powerset(sk5)) ) )
& element(sk6,powerset(sk5)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5,sk6])],[f38_nnf]) ).
cnf(c77,plain,
element(sk6,powerset(sk5)),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(p1222,plain,
( sk6 = sk5
| proper_element(sk6,powerset(sk5)) ),
inference(resolution,[status(thm)],[c41,c77]) ).
cnf(c80,plain,
( ~ proper_element(sk6,powerset(sk5))
| sk6 = sk5 ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(p1227,plain,
( sk6 = sk5
| sk6 = sk5 ),
inference(resolution,[status(thm)],[p1222,c80]) ).
cnf(p1228,plain,
sk6 = sk5,
inference(factoring,[status(thm)],[p1227]) ).
cnf(c79,plain,
( sk6 != sk5
| proper_element(sk6,powerset(sk5)) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(p1229,plain,
( sk5 != sk5
| proper_element(sk5,powerset(sk5)) ),
inference(demodulation,[status(thm)],[p1228,c79]) ).
cnf(p1230,plain,
proper_element(sk5,powerset(sk5)),
inference(equality_resolution,[status(thm)],[p1229]) ).
cnf(c40,plain,
( X1 != union(X0)
| ~ proper_element(X1,X0)
| ~ element(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
fof(f35,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f35_nnf,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c74,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
fof(f32,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f32_nnf,plain,
! [A,B] : subset(A,A),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [A] : subset(A,A),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c70,plain,
subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(p100,plain,
element(X0,powerset(X0)),
inference(resolution,[status(thm)],[c74,c70]) ).
cnf(p1220,plain,
( X0 != X0
| ~ proper_element(X0,powerset(X0)) ),
inference(resolution,[status(thm)],[c40,p100]) ).
cnf(p1221,plain,
~ proper_element(X0,powerset(X0)),
inference(equality_resolution,[status(thm)],[p1220]) ).
cnf(p1231,plain,
$false,
inference(resolution,[status(thm)],[p1230,p1221]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU354+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 13:52:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.21/4.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.21/4.01 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------