%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET002-1 : TPTP v9.3.1. Released v1.0.0.
% 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 02:41:25 PM UTC 2026
% Result : Unsatisfiable 4.55s 1.08s
% Output : Proof 4.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 11 unt; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 81 ( 36 ~; 45 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 61 ( 2 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f6,axiom,
( member(Element,Set2)
| member(Element,Set1)
| ~ member(Element,Union)
| ~ union(Set1,Set2,Union) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_union_is_member_of_one_set) ).
fof(f6_nnf,plain,
! [Set1,Set2,Union,Element] :
( member(Element,Set2)
| member(Element,Set1)
| ~ member(Element,Union)
| ~ union(Set1,Set2,Union) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [Set1,Set2,Union,Element] :
( member(Element,Set2)
| member(Element,Set1)
| ~ member(Element,Union)
| ~ union(Set1,Set2,Union) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( member(X3,X1)
| member(X3,X0)
| ~ member(X3,X2)
| ~ union(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(f12,hypothesis,
union(a,a,aUa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_union_a_is_aUa) ).
fof(f12_nnf,plain,
union(a,a,aUa),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
union(a,a,aUa),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(p22,plain,
( member(X0,a)
| member(X0,a)
| ~ member(X0,aUa) ),
inference(resolution,[status(thm)],[c6,c12]) ).
cnf(p27,plain,
( member(X0,a)
| ~ member(X0,aUa) ),
inference(factoring,[status(thm)],[p22]) ).
cnf(f1,axiom,
( member(member_of_1_not_of_2(Subset,Superset),Subset)
| subset(Subset,Superset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom1) ).
fof(f1_nnf,plain,
! [Subset,Superset] :
( member(member_of_1_not_of_2(Subset,Superset),Subset)
| subset(Subset,Superset) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [Subset,Superset] :
( member(member_of_1_not_of_2(Subset,Superset),Subset)
| subset(Subset,Superset) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( member(member_of_1_not_of_2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p28,plain,
( subset(aUa,X0)
| member(member_of_1_not_of_2(aUa,X0),a) ),
inference(resolution,[status(thm)],[p27,c1]) ).
cnf(f2,axiom,
( subset(Subset,Superset)
| ~ member(member_of_1_not_of_2(Subset,Superset),Superset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom2) ).
fof(f2_nnf,plain,
! [Subset,Superset] :
( subset(Subset,Superset)
| ~ member(member_of_1_not_of_2(Subset,Superset),Superset) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [Subset,Superset] :
( subset(Subset,Superset)
| ~ member(member_of_1_not_of_2(Subset,Superset),Superset) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p30,plain,
( subset(aUa,a)
| subset(aUa,a) ),
inference(resolution,[status(thm)],[p28,c2]) ).
cnf(p31,plain,
subset(aUa,a),
inference(factoring,[status(thm)],[p30]) ).
cnf(f7,axiom,
( member(Element,Union)
| ~ member(Element,Set1)
| ~ union(Set1,Set2,Union) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set1_is_member_of_union) ).
fof(f7_nnf,plain,
! [Set1,Set2,Union,Element] :
( member(Element,Union)
| ~ member(Element,Set1)
| ~ union(Set1,Set2,Union) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [Set1,Set2,Union,Element] :
( member(Element,Union)
| ~ member(Element,Set1)
| ~ union(Set1,Set2,Union) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( member(X3,X2)
| ~ member(X3,X0)
| ~ union(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p19,plain,
( member(X0,aUa)
| ~ member(X0,a) ),
inference(resolution,[status(thm)],[c7,c12]) ).
cnf(p20,plain,
( subset(a,X0)
| member(member_of_1_not_of_2(a,X0),aUa) ),
inference(resolution,[status(thm)],[p19,c1]) ).
cnf(p24,plain,
( subset(a,aUa)
| subset(a,aUa) ),
inference(resolution,[status(thm)],[p20,c2]) ).
cnf(p25,plain,
subset(a,aUa),
inference(factoring,[status(thm)],[p24]) ).
cnf(f5,axiom,
( equal_sets(Set2,Set1)
| ~ subset(Set2,Set1)
| ~ subset(Set1,Set2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_are_set_equal_sets) ).
fof(f5_nnf,plain,
! [Set1,Set2] :
( equal_sets(Set2,Set1)
| ~ subset(Set2,Set1)
| ~ subset(Set1,Set2) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [Set1,Set2] :
( equal_sets(Set2,Set1)
| ~ subset(Set2,Set1)
| ~ subset(Set1,Set2) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( equal_sets(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p26,plain,
( equal_sets(aUa,a)
| ~ subset(aUa,a) ),
inference(resolution,[status(thm)],[p25,c5]) ).
cnf(p45,plain,
equal_sets(aUa,a),
inference(resolution,[status(thm)],[p31,p26]) ).
cnf(f13,negated_conjecture,
~ equal_sets(aUa,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_equals_aUa) ).
fof(f13_nnf,plain,
~ equal_sets(aUa,a),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
~ equal_sets(aUa,a),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
~ equal_sets(aUa,a),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p46,plain,
$false,
inference(resolution,[status(thm)],[p45,c13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.37 % Computer : n009.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 09:03:58 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.55/1.08 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.55/1.08 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------