%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET005-1 : 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 02:41:26 PM UTC 2026
% Result : Unsatisfiable 4.77s 1.21s
% Output : Proof 4.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 13
% Syntax : Number of formulae : 90 ( 17 unt; 0 def)
% Number of atoms : 218 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 209 ( 81 ~; 128 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 147 ( 4 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f10,axiom,
( member(h(Set1,Set2,Intersection),Set2)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_axiom2) ).
fof(f10_nnf,plain,
! [Set1,Set2,Intersection] :
( member(h(Set1,Set2,Intersection),Set2)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [Set1,Set2,Intersection] :
( member(h(Set1,Set2,Intersection),Set2)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( member(h(X0,X1,X2),X1)
| intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
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(p64,plain,
( member(h(X0,X1,X2),X3)
| ~ subset(X2,X3)
| member(h(X0,X1,X2),X1)
| intersection(X0,X1,X2) ),
inference(resolution,[status(thm)],[c10,c0]) ).
cnf(p291,plain,
( ~ subset(X2,X1)
| member(h(X0,X1,X2),X1)
| intersection(X0,X1,X2) ),
inference(factoring,[status(thm)],[p64]) ).
cnf(f7,axiom,
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set2) ).
fof(f7_nnf,plain,
! [Set1,Set2,Intersection,Element] :
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [Set1,Set2,Intersection,Element] :
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( member(X3,X1)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(f14,axiom,
intersection(a,bIc,aIbIc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_bIc) ).
fof(f14_nnf,plain,
intersection(a,bIc,aIbIc),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c14,plain,
intersection(a,bIc,aIbIc),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(p31,plain,
( member(X0,bIc)
| ~ member(X0,aIbIc) ),
inference(resolution,[status(thm)],[c7,c14]) ).
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(p40,plain,
( subset(aIbIc,X0)
| member(member_of_1_not_of_2(aIbIc,X0),bIc) ),
inference(resolution,[status(thm)],[p31,c1]) ).
cnf(f13,axiom,
intersection(b,c,bIc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_intersection_c) ).
fof(f13_nnf,plain,
intersection(b,c,bIc),
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c13,plain,
intersection(b,c,bIc),
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(p30,plain,
( member(X0,c)
| ~ member(X0,bIc) ),
inference(resolution,[status(thm)],[c7,c13]) ).
cnf(p93,plain,
( member(member_of_1_not_of_2(aIbIc,X0),c)
| subset(aIbIc,X0) ),
inference(resolution,[status(thm)],[p40,p30]) ).
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(p101,plain,
( subset(aIbIc,c)
| subset(aIbIc,c) ),
inference(resolution,[status(thm)],[p93,c2]) ).
cnf(p102,plain,
subset(aIbIc,c),
inference(factoring,[status(thm)],[p101]) ).
cnf(p432,plain,
( member(h(X0,c,aIbIc),c)
| intersection(X0,c,aIbIc) ),
inference(resolution,[status(thm)],[p291,p102]) ).
cnf(f8,axiom,
( member(Element,Intersection)
| ~ member(Element,Set1)
| ~ member(Element,Set2)
| ~ intersection(Set1,Set2,Intersection) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_both_is_member_of_intersection) ).
fof(f8_nnf,plain,
! [Set1,Set2,Intersection,Element] :
( member(Element,Intersection)
| ~ member(Element,Set1)
| ~ member(Element,Set2)
| ~ intersection(Set1,Set2,Intersection) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [Set1,Set2,Intersection,Element] :
( member(Element,Intersection)
| ~ member(Element,Set1)
| ~ member(Element,Set2)
| ~ intersection(Set1,Set2,Intersection) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( member(X3,X2)
| ~ member(X3,X0)
| ~ member(X3,X1)
| ~ intersection(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p38,plain,
( member(X0,bIc)
| ~ member(X0,b)
| ~ member(X0,c) ),
inference(resolution,[status(thm)],[c8,c13]) ).
cnf(p446,plain,
( member(h(X0,c,aIbIc),bIc)
| ~ member(h(X0,c,aIbIc),b)
| intersection(X0,c,aIbIc) ),
inference(resolution,[status(thm)],[p432,p38]) ).
cnf(f9,axiom,
( member(h(Set1,Set2,Intersection),Set1)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_axiom1) ).
fof(f9_nnf,plain,
! [Set1,Set2,Intersection] :
( member(h(Set1,Set2,Intersection),Set1)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [Set1,Set2,Intersection] :
( member(h(Set1,Set2,Intersection),Set1)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( member(h(X0,X1,X2),X0)
| intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p45,plain,
( member(h(X0,X1,X2),X3)
| ~ subset(X2,X3)
| member(h(X0,X1,X2),X0)
| intersection(X0,X1,X2) ),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(p144,plain,
( ~ subset(X2,X0)
| member(h(X0,X1,X2),X0)
| intersection(X0,X1,X2) ),
inference(factoring,[status(thm)],[p45]) ).
cnf(f12,axiom,
intersection(a,b,aIb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_b) ).
fof(f12_nnf,plain,
intersection(a,b,aIb),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
intersection(a,b,aIb),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(p37,plain,
( member(X0,aIb)
| ~ member(X0,a)
| ~ member(X0,b) ),
inference(resolution,[status(thm)],[c8,c12]) ).
cnf(f6,axiom,
( member(Element,Set1)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set1) ).
fof(f6_nnf,plain,
! [Set1,Set2,Intersection,Element] :
( member(Element,Set1)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [Set1,Set2,Intersection,Element] :
( member(Element,Set1)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( member(X3,X0)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p22,plain,
( member(X0,b)
| ~ member(X0,bIc) ),
inference(resolution,[status(thm)],[c6,c13]) ).
cnf(p92,plain,
( member(member_of_1_not_of_2(aIbIc,X0),b)
| subset(aIbIc,X0) ),
inference(resolution,[status(thm)],[p40,p22]) ).
cnf(p109,plain,
( subset(aIbIc,X0)
| member(member_of_1_not_of_2(aIbIc,X0),aIb)
| ~ member(member_of_1_not_of_2(aIbIc,X0),a) ),
inference(resolution,[status(thm)],[p37,p92]) ).
cnf(p23,plain,
( member(X0,a)
| ~ member(X0,aIbIc) ),
inference(resolution,[status(thm)],[c6,c14]) ).
cnf(p26,plain,
( subset(aIbIc,X0)
| member(member_of_1_not_of_2(aIbIc,X0),a) ),
inference(resolution,[status(thm)],[p23,c1]) ).
cnf(p214,plain,
( subset(aIbIc,X0)
| subset(aIbIc,X0)
| member(member_of_1_not_of_2(aIbIc,X0),aIb) ),
inference(resolution,[status(thm)],[p109,p26]) ).
cnf(p223,plain,
( subset(aIbIc,X0)
| member(member_of_1_not_of_2(aIbIc,X0),aIb) ),
inference(factoring,[status(thm)],[p214]) ).
cnf(p225,plain,
( subset(aIbIc,aIb)
| subset(aIbIc,aIb) ),
inference(resolution,[status(thm)],[p223,c2]) ).
cnf(p226,plain,
subset(aIbIc,aIb),
inference(factoring,[status(thm)],[p225]) ).
cnf(p265,plain,
( member(h(aIb,X0,aIbIc),aIb)
| intersection(aIb,X0,aIbIc) ),
inference(resolution,[status(thm)],[p144,p226]) ).
cnf(p29,plain,
( member(X0,b)
| ~ member(X0,aIb) ),
inference(resolution,[status(thm)],[c7,c12]) ).
cnf(p280,plain,
( member(h(aIb,X0,aIbIc),b)
| intersection(aIb,X0,aIbIc) ),
inference(resolution,[status(thm)],[p265,p29]) ).
cnf(p679,plain,
( intersection(aIb,c,aIbIc)
| member(h(aIb,c,aIbIc),bIc)
| intersection(aIb,c,aIbIc) ),
inference(resolution,[status(thm)],[p446,p280]) ).
cnf(p685,plain,
( member(h(aIb,c,aIbIc),bIc)
| intersection(aIb,c,aIbIc) ),
inference(factoring,[status(thm)],[p679]) ).
cnf(p39,plain,
( member(X0,aIbIc)
| ~ member(X0,a)
| ~ member(X0,bIc) ),
inference(resolution,[status(thm)],[c8,c14]) ).
cnf(p687,plain,
( member(h(aIb,c,aIbIc),aIbIc)
| ~ member(h(aIb,c,aIbIc),a)
| intersection(aIb,c,aIbIc) ),
inference(resolution,[status(thm)],[p685,p39]) ).
cnf(p21,plain,
( member(X0,a)
| ~ member(X0,aIb) ),
inference(resolution,[status(thm)],[c6,c12]) ).
cnf(p279,plain,
( member(h(aIb,X0,aIbIc),a)
| intersection(aIb,X0,aIbIc) ),
inference(resolution,[status(thm)],[p265,p21]) ).
cnf(p712,plain,
( intersection(aIb,c,aIbIc)
| member(h(aIb,c,aIbIc),aIbIc)
| intersection(aIb,c,aIbIc) ),
inference(resolution,[status(thm)],[p687,p279]) ).
cnf(p714,plain,
( member(h(aIb,c,aIbIc),aIbIc)
| intersection(aIb,c,aIbIc) ),
inference(factoring,[status(thm)],[p712]) ).
cnf(f11,axiom,
( intersection(Set1,Set2,Intersection)
| ~ member(h(Set1,Set2,Intersection),Set1)
| ~ member(h(Set1,Set2,Intersection),Set2)
| ~ member(h(Set1,Set2,Intersection),Intersection) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_axiom3) ).
fof(f11_nnf,plain,
! [Set1,Set2,Intersection] :
( intersection(Set1,Set2,Intersection)
| ~ member(h(Set1,Set2,Intersection),Set1)
| ~ member(h(Set1,Set2,Intersection),Set2)
| ~ member(h(Set1,Set2,Intersection),Intersection) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [Set1,Set2,Intersection] :
( intersection(Set1,Set2,Intersection)
| ~ member(h(Set1,Set2,Intersection),Set1)
| ~ member(h(Set1,Set2,Intersection),Set2)
| ~ member(h(Set1,Set2,Intersection),Intersection) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( intersection(X0,X1,X2)
| ~ member(h(X0,X1,X2),X0)
| ~ member(h(X0,X1,X2),X1)
| ~ member(h(X0,X1,X2),X2) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p716,plain,
( intersection(aIb,c,aIbIc)
| ~ member(h(aIb,c,aIbIc),aIb)
| ~ member(h(aIb,c,aIbIc),c)
| intersection(aIb,c,aIbIc) ),
inference(resolution,[status(thm)],[p714,c11]) ).
cnf(p893,plain,
( ~ member(h(aIb,c,aIbIc),aIb)
| ~ member(h(aIb,c,aIbIc),c)
| intersection(aIb,c,aIbIc) ),
inference(factoring,[status(thm)],[p716]) ).
cnf(p899,plain,
( intersection(aIb,c,aIbIc)
| ~ member(h(aIb,c,aIbIc),aIb)
| intersection(aIb,c,aIbIc) ),
inference(resolution,[status(thm)],[p893,p432]) ).
cnf(p900,plain,
( ~ member(h(aIb,c,aIbIc),aIb)
| intersection(aIb,c,aIbIc) ),
inference(factoring,[status(thm)],[p899]) ).
cnf(p901,plain,
( intersection(aIb,c,aIbIc)
| intersection(aIb,c,aIbIc) ),
inference(resolution,[status(thm)],[p900,p265]) ).
cnf(p902,plain,
intersection(aIb,c,aIbIc),
inference(factoring,[status(thm)],[p901]) ).
cnf(f15,negated_conjecture,
~ intersection(aIb,c,aIbIc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_aIb_intersection_c_is_aIbIc) ).
fof(f15_nnf,plain,
~ intersection(aIb,c,aIbIc),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
~ intersection(aIb,c,aIbIc),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
~ intersection(aIb,c,aIbIc),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p904,plain,
$false,
inference(resolution,[status(thm)],[p902,c15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 09:04:28 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.77/1.21 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.77/1.21 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------