%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET012-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 02:41:27 PM UTC 2026
% Result : Unsatisfiable 111.00s 17.63s
% Output : Proof 111.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 8 unt; 0 def)
% Number of atoms : 66 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 58 ( 27 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f3,axiom,
( subset(Subset,Superset)
| ~ member(member_of_1_not_of_2(Subset,Superset),Superset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom2) ).
fof(f3_nnf,plain,
! [Subset,Superset] :
( subset(Subset,Superset)
| ~ member(member_of_1_not_of_2(Subset,Superset),Superset) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [Subset,Superset] :
( subset(Subset,Superset)
| ~ member(member_of_1_not_of_2(Subset,Superset),Superset) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(f4,axiom,
( member(X,complement(Xs))
| member(X,Xs) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set_or_complement) ).
fof(f4_nnf,plain,
! [X,Xs] :
( member(X,complement(Xs))
| member(X,Xs) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Xs] :
( member(X,complement(Xs))
| member(X,Xs) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( member(X0,complement(X1))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p28,plain,
( member(member_of_1_not_of_2(X0,complement(X1)),X1)
| subset(X0,complement(X1)) ),
inference(resolution,[status(thm)],[c3,c4]) ).
cnf(f5,axiom,
( ~ member(X,complement(Xs))
| ~ member(X,Xs) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_member_of_set_and_complement) ).
fof(f5_nnf,plain,
! [X,Xs] :
( ~ member(X,complement(Xs))
| ~ member(X,Xs) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Xs] :
( ~ member(X,complement(Xs))
| ~ member(X,Xs) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f2,axiom,
( member(member_of_1_not_of_2(Subset,Superset),Subset)
| subset(Subset,Superset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom1) ).
fof(f2_nnf,plain,
! [Subset,Superset] :
( member(member_of_1_not_of_2(Subset,Superset),Subset)
| subset(Subset,Superset) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [Subset,Superset] :
( member(member_of_1_not_of_2(Subset,Superset),Subset)
| subset(Subset,Superset) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( member(member_of_1_not_of_2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p26,plain,
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),complement(X0)) ),
inference(resolution,[status(thm)],[c5,c2]) ).
cnf(p68,plain,
( subset(X0,complement(complement(X0)))
| subset(X0,complement(complement(X0))) ),
inference(resolution,[status(thm)],[p28,p26]) ).
cnf(p1046,plain,
subset(X0,complement(complement(X0))),
inference(factoring,[status(thm)],[p68]) ).
cnf(f14,axiom,
( equal_sets(Set2,Set1)
| ~ subset(Set2,Set1)
| ~ subset(Set1,Set2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_are_set_equal_sets) ).
fof(f14_nnf,plain,
! [Set1,Set2] :
( equal_sets(Set2,Set1)
| ~ subset(Set2,Set1)
| ~ subset(Set1,Set2) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [Set1,Set2] :
( equal_sets(Set2,Set1)
| ~ subset(Set2,Set1)
| ~ subset(Set1,Set2) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( equal_sets(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p1047,plain,
( equal_sets(complement(complement(X0)),X0)
| ~ subset(complement(complement(X0)),X0) ),
inference(resolution,[status(thm)],[p1046,c14]) ).
cnf(p27,plain,
( member(X0,X1)
| ~ member(X0,complement(complement(X1))) ),
inference(resolution,[status(thm)],[c5,c4]) ).
cnf(p37,plain,
( subset(complement(complement(X0)),X1)
| member(member_of_1_not_of_2(complement(complement(X0)),X1),X0) ),
inference(resolution,[status(thm)],[p27,c2]) ).
cnf(p204,plain,
( subset(complement(complement(X0)),X0)
| subset(complement(complement(X0)),X0) ),
inference(resolution,[status(thm)],[p37,c3]) ).
cnf(p6414,plain,
subset(complement(complement(X0)),X0),
inference(factoring,[status(thm)],[p204]) ).
cnf(p16036,plain,
equal_sets(complement(complement(X0)),X0),
inference(resolution,[status(thm)],[p1047,p6414]) ).
cnf(f21,negated_conjecture,
~ equal_sets(complement(complement(a)),a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_involution) ).
fof(f21_nnf,plain,
~ equal_sets(complement(complement(a)),a),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
~ equal_sets(complement(complement(a)),a),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
~ equal_sets(complement(complement(a)),a),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p16065,plain,
$false,
inference(resolution,[status(thm)],[p16036,c21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET012-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 09:04:49 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 111.00/17.63 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 111.00/17.63 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------