%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : 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 02:41:26 PM UTC 2026
% Result : Unsatisfiable 5.34s 6.13s
% Output : Proof 5.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 50 ( 15 unt; 0 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 113 ( 51 ~; 62 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 87 ( 7 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f8,axiom,
( member(Element,Set2)
| member(Element,Difference)
| ~ difference(Set1,Set2,Difference)
| ~ member(Element,Set1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_difference_or_set2) ).
fof(f8_nnf,plain,
! [Element,Set1,Set2,Difference] :
( member(Element,Set2)
| member(Element,Difference)
| ~ difference(Set1,Set2,Difference)
| ~ member(Element,Set1) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [Element,Set1,Set2,Difference] :
( member(Element,Set2)
| member(Element,Difference)
| ~ difference(Set1,Set2,Difference)
| ~ member(Element,Set1) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( member(X0,X2)
| member(X0,X3)
| ~ difference(X1,X2,X3)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(f6,axiom,
( member(Element,Set1)
| ~ member(Element,Difference)
| ~ difference(Set1,Set2,Difference) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_difference) ).
fof(f6_nnf,plain,
! [Set1,Set2,Difference,Element] :
( member(Element,Set1)
| ~ member(Element,Difference)
| ~ difference(Set1,Set2,Difference) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [Set1,Set2,Difference,Element] :
( member(Element,Set1)
| ~ member(Element,Difference)
| ~ difference(Set1,Set2,Difference) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( member(X3,X0)
| ~ member(X3,X2)
| ~ difference(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(f13,hypothesis,
difference(b,a,bDa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_minus_a) ).
fof(f13_nnf,plain,
difference(b,a,bDa),
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c13,plain,
difference(b,a,bDa),
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(p22,plain,
( member(X0,b)
| ~ member(X0,bDa) ),
inference(resolution,[status(thm)],[c6,c13]) ).
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(p24,plain,
( subset(bDa,X0)
| member(member_of_1_not_of_2(bDa,X0),b) ),
inference(resolution,[status(thm)],[p22,c1]) ).
cnf(p37,plain,
( subset(bDa,X2)
| member(member_of_1_not_of_2(bDa,X2),X0)
| member(member_of_1_not_of_2(bDa,X2),X1)
| ~ difference(b,X0,X1) ),
inference(resolution,[status(thm)],[c8,p24]) ).
cnf(f14,hypothesis,
difference(b,d,bDd),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_minus_d) ).
fof(f14_nnf,plain,
difference(b,d,bDd),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c14,plain,
difference(b,d,bDd),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(p98,plain,
( subset(bDa,X0)
| member(member_of_1_not_of_2(bDa,X0),d)
| member(member_of_1_not_of_2(bDa,X0),bDd) ),
inference(resolution,[status(thm)],[p37,c14]) ).
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(p260,plain,
( subset(bDa,bDd)
| subset(bDa,bDd)
| member(member_of_1_not_of_2(bDa,bDd),d) ),
inference(resolution,[status(thm)],[p98,c2]) ).
cnf(p267,plain,
( subset(bDa,bDd)
| member(member_of_1_not_of_2(bDa,bDd),d) ),
inference(factoring,[status(thm)],[p260]) ).
cnf(f0,axiom,
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',membership_in_subsets) ).
fof(f0_nnf,plain,
! [Element,Subset,Superset] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [Element,Subset,Superset] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p269,plain,
( member(member_of_1_not_of_2(bDa,bDd),X0)
| ~ subset(d,X0)
| subset(bDa,bDd) ),
inference(resolution,[status(thm)],[p267,c0]) ).
cnf(f12,hypothesis,
subset(d,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_is_a_subset_of_a) ).
fof(f12_nnf,plain,
subset(d,a),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
subset(d,a),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(p279,plain,
( member(member_of_1_not_of_2(bDa,bDd),a)
| subset(bDa,bDd) ),
inference(resolution,[status(thm)],[p269,c12]) ).
cnf(f7,axiom,
( ~ difference(A_set,Set1,Set2)
| ~ member(Element,Set2)
| ~ member(Element,Set1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_member_of_difference) ).
fof(f7_nnf,plain,
! [Element,Set1,Set2,A_set] :
( ~ difference(A_set,Set1,Set2)
| ~ member(Element,Set2)
| ~ member(Element,Set1) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [Element,Set1,Set2,A_set] :
( ~ difference(A_set,Set1,Set2)
| ~ member(Element,Set2)
| ~ member(Element,Set1) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ difference(X3,X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p281,plain,
( ~ difference(X1,a,X0)
| ~ member(member_of_1_not_of_2(bDa,bDd),X0)
| subset(bDa,bDd) ),
inference(resolution,[status(thm)],[p279,c7]) ).
cnf(p301,plain,
( subset(bDa,bDd)
| ~ difference(X0,a,bDa)
| subset(bDa,bDd) ),
inference(resolution,[status(thm)],[p281,c1]) ).
cnf(p304,plain,
( ~ difference(X0,a,bDa)
| subset(bDa,bDd) ),
inference(factoring,[status(thm)],[p301]) ).
cnf(p305,plain,
subset(bDa,bDd),
inference(resolution,[status(thm)],[p304,c13]) ).
cnf(f15,negated_conjecture,
~ subset(bDa,bDd),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_bDa_is_a_subset_of_bDd) ).
fof(f15_nnf,plain,
~ subset(bDa,bDd),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
~ subset(bDa,bDd),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
~ subset(bDa,bDd),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p306,plain,
$false,
inference(resolution,[status(thm)],[p305,c15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/5.36 % Computer : n014.cluster.edu
% 0.11/5.36 % Model : x86_64 x86_64
% 0.11/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.36 % Memory : 8046.5625MB
% 0.11/5.36 % OS : Linux 6.8.0-71-generic
% 0.11/5.36 % CPULimit : 300
% 0.11/5.36 % WCLimit : 300
% 0.11/5.36 % DateTime : Thu Sep 24 09:04:09 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.34/6.13 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.34/6.13 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------