%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU326+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 02:51:44 PM UTC 2026
% Result : Theorem 12.09s 4.20s
% Output : Proof 12.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 10 unt; 0 def)
% Number of atoms : 78 ( 46 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 78 ( 36 ~; 21 |; 16 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 5 sgn 22 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f32,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_setfam_1) ).
fof(f32_nnf,plain,
! [A,B] :
( complements_of_subsets(A,B) != empty_set
| B = empty_set
| ~ element(B,powerset(powerset(A))) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [B,A] :
( complements_of_subsets(A,B) != empty_set
| B = empty_set
| ~ element(B,powerset(powerset(A))) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c73,plain,
( complements_of_subsets(X0,X1) != empty_set
| X1 = empty_set
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
fof(f18,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(complements_of_subsets(A,B),powerset(powerset(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(f18_nnf,plain,
! [A,B] :
( element(complements_of_subsets(A,B),powerset(powerset(A)))
| ~ element(B,powerset(powerset(A))) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [B,A] :
( element(complements_of_subsets(A,B),powerset(powerset(A)))
| ~ element(B,powerset(powerset(A))) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c42,plain,
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f35,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f35_nnf,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c76,plain,
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
fof(f26,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f26_nnf,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [A] :
( empty(sk3(A))
& element(sk3(A),powerset(A)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3])],[f26_nnf]) ).
cnf(c62,plain,
empty(sk3(X0)),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p94,plain,
sk3(X0) = empty_set,
inference(resolution,[status(thm)],[c76,c62]) ).
cnf(c61,plain,
element(sk3(X0),powerset(X0)),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p95,plain,
element(empty_set,powerset(X0)),
inference(demodulation,[status(thm)],[p94,c61]) ).
cnf(p205,plain,
element(complements_of_subsets(X0,empty_set),powerset(powerset(X0))),
inference(resolution,[status(thm)],[c42,p95]) ).
cnf(p243,plain,
( empty_set != empty_set
| complements_of_subsets(X0,empty_set) = empty_set ),
inference(resolution,[status(thm)],[c73,p205]) ).
cnf(p271,plain,
complements_of_subsets(X0,empty_set) = empty_set,
inference(equality_resolution,[status(thm)],[p243]) ).
fof(f28,conjecture,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( ~ ( B = empty_set
& complements_of_subsets(A,B) != empty_set )
& ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_tops_2) ).
fof(f28_neg,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(powerset(A)))
=> ( ~ ( B = empty_set
& complements_of_subsets(A,B) != empty_set )
& ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f28_nnf,plain,
? [A,B] :
( ( ( B = empty_set
& complements_of_subsets(A,B) != empty_set )
| ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) )
& element(B,powerset(powerset(A))) ),
inference(nnf_transformation,[status(thm)],[f28_neg]) ).
fof(f28_sk,plain,
( ( ( sk5 = empty_set
& complements_of_subsets(sk4,sk5) != empty_set )
| ( complements_of_subsets(sk4,sk5) = empty_set
& sk5 != empty_set ) )
& element(sk5,powerset(powerset(sk4))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5])],[f28_nnf]) ).
cnf(c64,plain,
element(sk5,powerset(powerset(sk4))),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p239,plain,
( complements_of_subsets(sk4,sk5) != empty_set
| sk5 = empty_set ),
inference(resolution,[status(thm)],[c73,c64]) ).
cnf(c68,plain,
( sk5 = empty_set
| complements_of_subsets(sk4,sk5) = empty_set ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p264,plain,
( sk5 = empty_set
| sk5 = empty_set ),
inference(resolution,[status(thm)],[p239,c68]) ).
cnf(p265,plain,
sk5 = empty_set,
inference(factoring,[status(thm)],[p264]) ).
cnf(c65,plain,
( complements_of_subsets(sk4,sk5) != empty_set
| sk5 != empty_set ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p266,plain,
( complements_of_subsets(sk4,empty_set) != empty_set
| empty_set != empty_set ),
inference(demodulation,[status(thm)],[p265,c65]) ).
cnf(p274,plain,
( empty_set != empty_set
| empty_set != empty_set ),
inference(demodulation,[status(thm)],[p271,p266]) ).
cnf(p276,plain,
empty_set != empty_set,
inference(factoring,[status(thm)],[p274]) ).
cnf(p277,plain,
$false,
inference(equality_resolution,[status(thm)],[p276]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU326+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.41 % Computer : n007.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Thu Sep 24 13:40:53 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 12.09/4.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.09/4.20 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------