%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET012-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 211.65s 31.56s
% Output : Proof 211.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 88 ( 25 unt; 0 def)
% Number of atoms : 165 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 139 ( 62 ~; 77 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 120 ( 0 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(p34,plain,
( subset(X0,complement(X1))
| member(member_of_1_not_of_2(X0,complement(X1)),X1) ),
inference(resolution,[status(thm)],[c4,c3]) ).
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(p35,plain,
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),complement(X0)) ),
inference(resolution,[status(thm)],[c5,c2]) ).
cnf(p78,plain,
( subset(X0,complement(complement(X0)))
| subset(X0,complement(complement(X0))) ),
inference(resolution,[status(thm)],[p34,p35]) ).
cnf(p1092,plain,
subset(X0,complement(complement(X0))),
inference(factoring,[status(thm)],[p78]) ).
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(p1093,plain,
( equal_sets(complement(complement(X0)),X0)
| ~ subset(complement(complement(X0)),X0) ),
inference(resolution,[status(thm)],[p1092,c14]) ).
cnf(p36,plain,
( member(X0,X1)
| ~ member(X0,complement(complement(X1))) ),
inference(resolution,[status(thm)],[c5,c4]) ).
cnf(p43,plain,
( subset(complement(complement(X0)),X1)
| member(member_of_1_not_of_2(complement(complement(X0)),X1),X0) ),
inference(resolution,[status(thm)],[p36,c2]) ).
cnf(p215,plain,
( subset(complement(complement(X0)),X0)
| subset(complement(complement(X0)),X0) ),
inference(resolution,[status(thm)],[p43,c3]) ).
cnf(p4909,plain,
subset(complement(complement(X0)),X0),
inference(factoring,[status(thm)],[p215]) ).
cnf(p19404,plain,
equal_sets(complement(complement(X0)),X0),
inference(resolution,[status(thm)],[p1093,p4909]) ).
cnf(f16,axiom,
( equal_sets(Ys,Xs)
| ~ equal_sets(Xs,Ys) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_for_set_equal) ).
fof(f16_nnf,plain,
! [Xs,Ys] :
( equal_sets(Ys,Xs)
| ~ equal_sets(Xs,Ys) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [Xs,Ys] :
( equal_sets(Ys,Xs)
| ~ equal_sets(Xs,Ys) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( equal_sets(X1,X0)
| ~ equal_sets(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p19405,plain,
equal_sets(X0,complement(complement(X0))),
inference(resolution,[status(thm)],[p19404,c16]) ).
cnf(f17,axiom,
( equal_sets(Xs,Zs)
| ~ equal_sets(Ys,Zs)
| ~ equal_sets(Xs,Ys) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_set_equal) ).
fof(f17_nnf,plain,
! [Xs,Ys,Zs] :
( equal_sets(Xs,Zs)
| ~ equal_sets(Ys,Zs)
| ~ equal_sets(Xs,Ys) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [Xs,Ys,Zs] :
( equal_sets(Xs,Zs)
| ~ equal_sets(Ys,Zs)
| ~ equal_sets(Xs,Ys) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( equal_sets(X0,X2)
| ~ equal_sets(X1,X2)
| ~ equal_sets(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(f21,hypothesis,
equal_sets(complement(a),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_a_is_b) ).
fof(f21_nnf,plain,
equal_sets(complement(a),b),
inference(nnf_transformation,[status(thm)],[f21]) ).
cnf(c21,plain,
equal_sets(complement(a),b),
inference(cnf_transformation,[status(esa)],[f21_nnf]) ).
cnf(p67,plain,
( equal_sets(complement(a),X0)
| ~ equal_sets(b,X0) ),
inference(resolution,[status(thm)],[c17,c21]) ).
cnf(p19408,plain,
equal_sets(complement(a),complement(complement(b))),
inference(resolution,[status(thm)],[p19405,p67]) ).
cnf(f13,axiom,
( subset(Subset,Superset)
| ~ equal_sets(Superset,Subset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_equal_sets_are_subsets2) ).
fof(f13_nnf,plain,
! [Superset,Subset] :
( subset(Subset,Superset)
| ~ equal_sets(Superset,Subset) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [Superset,Subset] :
( subset(Subset,Superset)
| ~ equal_sets(Superset,Subset) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( subset(X1,X0)
| ~ equal_sets(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p19413,plain,
subset(complement(complement(b)),complement(a)),
inference(resolution,[status(thm)],[p19408,c13]) ).
cnf(f1,axiom,
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',membership_in_subsets) ).
fof(f1_nnf,plain,
! [Element,Subset,Superset] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [Element,Subset,Superset] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p33,plain,
( member(X0,X2)
| ~ subset(complement(X1),X2)
| member(X0,X1) ),
inference(resolution,[status(thm)],[c4,c1]) ).
cnf(p19549,plain,
( member(X0,complement(a))
| member(X0,complement(b)) ),
inference(resolution,[status(thm)],[p19413,p33]) ).
cnf(p21165,plain,
( ~ member(X0,complement(complement(b)))
| member(X0,complement(a)) ),
inference(resolution,[status(thm)],[p19549,c5]) ).
cnf(f22,hypothesis,
equal_sets(complement(b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_b_is_c) ).
fof(f22_nnf,plain,
equal_sets(complement(b),c),
inference(nnf_transformation,[status(thm)],[f22]) ).
cnf(c22,plain,
equal_sets(complement(b),c),
inference(cnf_transformation,[status(esa)],[f22_nnf]) ).
cnf(p32,plain,
equal_sets(c,complement(b)),
inference(resolution,[status(thm)],[c16,c22]) ).
cnf(p70,plain,
( equal_sets(c,X0)
| ~ equal_sets(complement(b),X0) ),
inference(resolution,[status(thm)],[c17,p32]) ).
cnf(p19411,plain,
equal_sets(c,complement(complement(complement(b)))),
inference(resolution,[status(thm)],[p19405,p70]) ).
cnf(p19448,plain,
subset(complement(complement(complement(b))),c),
inference(resolution,[status(thm)],[p19411,c13]) ).
cnf(p19716,plain,
( member(X0,c)
| member(X0,complement(complement(b))) ),
inference(resolution,[status(thm)],[p19448,p33]) ).
cnf(p23263,plain,
( member(X0,c)
| member(X0,complement(a)) ),
inference(resolution,[status(thm)],[p21165,p19716]) ).
cnf(p23274,plain,
( subset(a,X0)
| member(member_of_1_not_of_2(a,X0),c) ),
inference(resolution,[status(thm)],[p23263,p35]) ).
cnf(p23525,plain,
( subset(a,c)
| subset(a,c) ),
inference(resolution,[status(thm)],[p23274,c3]) ).
cnf(p23551,plain,
subset(a,c),
inference(factoring,[status(thm)],[p23525]) ).
cnf(f12,axiom,
( subset(Subset,Superset)
| ~ equal_sets(Subset,Superset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_equal_sets_are_subsets1) ).
fof(f12_nnf,plain,
! [Subset,Superset] :
( subset(Subset,Superset)
| ~ equal_sets(Subset,Superset) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [Subset,Superset] :
( subset(Subset,Superset)
| ~ equal_sets(Subset,Superset) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( subset(X0,X1)
| ~ equal_sets(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p25,plain,
subset(complement(a),b),
inference(resolution,[status(thm)],[c12,c21]) ).
cnf(p102,plain,
( member(X0,b)
| member(X0,a) ),
inference(resolution,[status(thm)],[p33,p25]) ).
cnf(p107,plain,
( ~ member(X0,complement(b))
| member(X0,a) ),
inference(resolution,[status(thm)],[p102,c5]) ).
cnf(p28,plain,
( member(member_of_1_not_of_2(X0,X1),X2)
| ~ subset(X0,X2)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[c2,c1]) ).
cnf(p30,plain,
subset(c,complement(b)),
inference(resolution,[status(thm)],[c13,c22]) ).
cnf(p86,plain,
( member(member_of_1_not_of_2(c,X0),complement(b))
| subset(c,X0) ),
inference(resolution,[status(thm)],[p28,p30]) ).
cnf(p382,plain,
( subset(c,X0)
| member(member_of_1_not_of_2(c,X0),a) ),
inference(resolution,[status(thm)],[p107,p86]) ).
cnf(p1521,plain,
( subset(c,a)
| subset(c,a) ),
inference(resolution,[status(thm)],[p382,c3]) ).
cnf(p1532,plain,
subset(c,a),
inference(factoring,[status(thm)],[p1521]) ).
cnf(p1533,plain,
( equal_sets(a,c)
| ~ subset(a,c) ),
inference(resolution,[status(thm)],[p1532,c14]) ).
cnf(p23553,plain,
equal_sets(a,c),
inference(resolution,[status(thm)],[p23551,p1533]) ).
cnf(f23,negated_conjecture,
~ equal_sets(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_equals_c) ).
fof(f23_nnf,plain,
~ equal_sets(a,c),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
~ equal_sets(a,c),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
~ equal_sets(a,c),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p23586,plain,
$false,
inference(resolution,[status(thm)],[p23553,c23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET012-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n001.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 09:10:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 211.65/31.56 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 211.65/31.56 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------