%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET010-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 62.96s 43.29s
% Output : Proof 62.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 20
% Syntax : Number of formulae : 144 ( 22 unt; 0 def)
% Number of atoms : 377 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 374 ( 141 ~; 233 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 269 ( 22 sgn 100 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f9,axiom,
( member(g(Set1,Set2,Union),Union)
| member(g(Set1,Set2,Union),Set2)
| member(g(Set1,Set2,Union),Set1)
| union(Set1,Set2,Union) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_axiom1) ).
fof(f9_nnf,plain,
! [Set1,Set2,Union] :
( member(g(Set1,Set2,Union),Union)
| member(g(Set1,Set2,Union),Set2)
| member(g(Set1,Set2,Union),Set1)
| union(Set1,Set2,Union) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [Set1,Set2,Union] :
( member(g(Set1,Set2,Union),Union)
| member(g(Set1,Set2,Union),Set2)
| member(g(Set1,Set2,Union),Set1)
| union(Set1,Set2,Union) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( member(g(X0,X1,X2),X2)
| member(g(X0,X1,X2),X1)
| member(g(X0,X1,X2),X0)
| union(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(f0,axiom,
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ),
file('/export/starexec/sandbox/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(p39,plain,
( member(g(X0,X1,X2),X3)
| ~ subset(X0,X3)
| member(g(X0,X1,X2),X2)
| member(g(X0,X1,X2),X1)
| union(X0,X1,X2) ),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(p337,plain,
( ~ subset(X0,X2)
| member(g(X0,X1,X2),X2)
| member(g(X0,X1,X2),X1)
| union(X0,X1,X2) ),
inference(factoring,[status(thm)],[p39]) ).
cnf(f20,axiom,
( member(Element,Set2)
| member(Element,Difference)
| ~ difference(Set1,Set2,Difference)
| ~ member(Element,Set1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_difference_or_set2) ).
fof(f20_nnf,plain,
! [Element,Set1,Set2,Difference] :
( member(Element,Set2)
| member(Element,Difference)
| ~ difference(Set1,Set2,Difference)
| ~ member(Element,Set1) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [Element,Set1,Set2,Difference] :
( member(Element,Set2)
| member(Element,Difference)
| ~ difference(Set1,Set2,Difference)
| ~ member(Element,Set1) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( member(X0,X2)
| member(X0,X3)
| ~ difference(X1,X2,X3)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(f18,axiom,
( member(Element,Set1)
| ~ member(Element,Difference)
| ~ difference(Set1,Set2,Difference) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_difference) ).
fof(f18_nnf,plain,
! [Set1,Set2,Difference,Element] :
( member(Element,Set1)
| ~ member(Element,Difference)
| ~ difference(Set1,Set2,Difference) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [Set1,Set2,Difference,Element] :
( member(Element,Set1)
| ~ member(Element,Difference)
| ~ difference(Set1,Set2,Difference) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( member(X3,X0)
| ~ member(X3,X2)
| ~ difference(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(f25,hypothesis,
difference(c,a,cDa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_minus_a) ).
fof(f25_nnf,plain,
difference(c,a,cDa),
inference(nnf_transformation,[status(thm)],[f25]) ).
cnf(c25,plain,
difference(c,a,cDa),
inference(cnf_transformation,[status(esa)],[f25_nnf]) ).
cnf(p67,plain,
( member(X0,c)
| ~ member(X0,cDa) ),
inference(resolution,[status(thm)],[c18,c25]) ).
cnf(f1,axiom,
( member(member_of_1_not_of_2(Subset,Superset),Subset)
| subset(Subset,Superset) ),
file('/export/starexec/sandbox/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(p70,plain,
( subset(cDa,X0)
| member(member_of_1_not_of_2(cDa,X0),c) ),
inference(resolution,[status(thm)],[p67,c1]) ).
cnf(p163,plain,
( subset(cDa,X2)
| member(member_of_1_not_of_2(cDa,X2),X0)
| member(member_of_1_not_of_2(cDa,X2),X1)
| ~ difference(c,X0,X1) ),
inference(resolution,[status(thm)],[c20,p70]) ).
cnf(f27,hypothesis,
difference(c,aIb,cD_aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_minus_aIb) ).
fof(f27_nnf,plain,
difference(c,aIb,cD_aIb),
inference(nnf_transformation,[status(thm)],[f27]) ).
cnf(c27,plain,
difference(c,aIb,cD_aIb),
inference(cnf_transformation,[status(esa)],[f27_nnf]) ).
cnf(p1473,plain,
( subset(cDa,X0)
| member(member_of_1_not_of_2(cDa,X0),aIb)
| member(member_of_1_not_of_2(cDa,X0),cD_aIb) ),
inference(resolution,[status(thm)],[p163,c27]) ).
cnf(f2,axiom,
( subset(Subset,Superset)
| ~ member(member_of_1_not_of_2(Subset,Superset),Superset) ),
file('/export/starexec/sandbox/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(p1814,plain,
( subset(cDa,cD_aIb)
| subset(cDa,cD_aIb)
| member(member_of_1_not_of_2(cDa,cD_aIb),aIb) ),
inference(resolution,[status(thm)],[p1473,c2]) ).
cnf(p1822,plain,
( subset(cDa,cD_aIb)
| member(member_of_1_not_of_2(cDa,cD_aIb),aIb) ),
inference(factoring,[status(thm)],[p1814]) ).
cnf(f12,axiom,
( member(Element,Set1)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set1) ).
fof(f12_nnf,plain,
! [Set1,Set2,Intersection,Element] :
( member(Element,Set1)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [Set1,Set2,Intersection,Element] :
( member(Element,Set1)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( member(X3,X0)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(f24,hypothesis,
intersection(a,b,aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_intersection_b) ).
fof(f24_nnf,plain,
intersection(a,b,aIb),
inference(nnf_transformation,[status(thm)],[f24]) ).
cnf(c24,plain,
intersection(a,b,aIb),
inference(cnf_transformation,[status(esa)],[f24_nnf]) ).
cnf(p35,plain,
( member(X0,a)
| ~ member(X0,aIb) ),
inference(resolution,[status(thm)],[c12,c24]) ).
cnf(p1824,plain,
( member(member_of_1_not_of_2(cDa,cD_aIb),a)
| subset(cDa,cD_aIb) ),
inference(resolution,[status(thm)],[p1822,p35]) ).
cnf(f19,axiom,
( ~ difference(A_set,Set1,Set2)
| ~ member(Element,Set2)
| ~ member(Element,Set1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_member_of_difference) ).
fof(f19_nnf,plain,
! [Element,Set1,Set2,A_set] :
( ~ difference(A_set,Set1,Set2)
| ~ member(Element,Set2)
| ~ member(Element,Set1) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [Element,Set1,Set2,A_set] :
( ~ difference(A_set,Set1,Set2)
| ~ member(Element,Set2)
| ~ member(Element,Set1) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( ~ difference(X3,X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p1833,plain,
( ~ difference(X1,a,X0)
| ~ member(member_of_1_not_of_2(cDa,cD_aIb),X0)
| subset(cDa,cD_aIb) ),
inference(resolution,[status(thm)],[p1824,c19]) ).
cnf(p1869,plain,
( subset(cDa,cD_aIb)
| ~ difference(X0,a,cDa)
| subset(cDa,cD_aIb) ),
inference(resolution,[status(thm)],[p1833,c1]) ).
cnf(p1873,plain,
( ~ difference(X0,a,cDa)
| subset(cDa,cD_aIb) ),
inference(factoring,[status(thm)],[p1869]) ).
cnf(p1876,plain,
subset(cDa,cD_aIb),
inference(resolution,[status(thm)],[p1873,c25]) ).
cnf(p2365,plain,
( member(g(cDa,X0,cD_aIb),cD_aIb)
| member(g(cDa,X0,cD_aIb),X0)
| union(cDa,X0,cD_aIb) ),
inference(resolution,[status(thm)],[p337,p1876]) ).
cnf(f26,hypothesis,
difference(c,b,cDb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_minus_b) ).
fof(f26_nnf,plain,
difference(c,b,cDb),
inference(nnf_transformation,[status(thm)],[f26]) ).
cnf(c26,plain,
difference(c,b,cDb),
inference(cnf_transformation,[status(esa)],[f26_nnf]) ).
cnf(p68,plain,
( member(X0,c)
| ~ member(X0,cDb) ),
inference(resolution,[status(thm)],[c18,c26]) ).
cnf(p85,plain,
( subset(cDb,X0)
| member(member_of_1_not_of_2(cDb,X0),c) ),
inference(resolution,[status(thm)],[p68,c1]) ).
cnf(p166,plain,
( subset(cDb,X2)
| member(member_of_1_not_of_2(cDb,X2),X0)
| member(member_of_1_not_of_2(cDb,X2),X1)
| ~ difference(c,X0,X1) ),
inference(resolution,[status(thm)],[c20,p85]) ).
cnf(p1505,plain,
( subset(cDb,X0)
| member(member_of_1_not_of_2(cDb,X0),aIb)
| member(member_of_1_not_of_2(cDb,X0),cD_aIb) ),
inference(resolution,[status(thm)],[p166,c27]) ).
cnf(p2312,plain,
( subset(cDb,cD_aIb)
| subset(cDb,cD_aIb)
| member(member_of_1_not_of_2(cDb,cD_aIb),aIb) ),
inference(resolution,[status(thm)],[p1505,c2]) ).
cnf(p2320,plain,
( subset(cDb,cD_aIb)
| member(member_of_1_not_of_2(cDb,cD_aIb),aIb) ),
inference(factoring,[status(thm)],[p2312]) ).
cnf(f13,axiom,
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_intersection_is_member_of_set2) ).
fof(f13_nnf,plain,
! [Set1,Set2,Intersection,Element] :
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [Set1,Set2,Intersection,Element] :
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( member(X3,X1)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p51,plain,
( member(X0,b)
| ~ member(X0,aIb) ),
inference(resolution,[status(thm)],[c13,c24]) ).
cnf(p2325,plain,
( member(member_of_1_not_of_2(cDb,cD_aIb),b)
| subset(cDb,cD_aIb) ),
inference(resolution,[status(thm)],[p2320,p51]) ).
cnf(p2340,plain,
( ~ difference(X1,b,X0)
| ~ member(member_of_1_not_of_2(cDb,cD_aIb),X0)
| subset(cDb,cD_aIb) ),
inference(resolution,[status(thm)],[p2325,c19]) ).
cnf(p2379,plain,
( subset(cDb,cD_aIb)
| ~ difference(X0,b,cDb)
| subset(cDb,cD_aIb) ),
inference(resolution,[status(thm)],[p2340,c1]) ).
cnf(p2383,plain,
( ~ difference(X0,b,cDb)
| subset(cDb,cD_aIb) ),
inference(factoring,[status(thm)],[p2379]) ).
cnf(p2386,plain,
subset(cDb,cD_aIb),
inference(resolution,[status(thm)],[p2383,c26]) ).
cnf(p37,plain,
( member(g(X0,X1,X0),X1)
| member(g(X0,X1,X0),X0)
| union(X0,X1,X0) ),
inference(factoring,[status(thm)],[c9]) ).
cnf(f10,axiom,
( union(Set1,Set2,Union)
| ~ member(g(Set1,Set2,Union),Union)
| ~ member(g(Set1,Set2,Union),Set1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_axiom2) ).
fof(f10_nnf,plain,
! [Set1,Set2,Union] :
( union(Set1,Set2,Union)
| ~ member(g(Set1,Set2,Union),Union)
| ~ member(g(Set1,Set2,Union),Set1) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [Set1,Set2,Union] :
( union(Set1,Set2,Union)
| ~ member(g(Set1,Set2,Union),Union)
| ~ member(g(Set1,Set2,Union),Set1) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X2)
| ~ member(g(X0,X1,X2),X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p50,plain,
( union(X0,X1,X0)
| ~ member(g(X0,X1,X0),X0) ),
inference(factoring,[status(thm)],[c10]) ).
cnf(p282,plain,
( union(X0,X1,X0)
| member(g(X0,X1,X0),X1)
| union(X0,X1,X0) ),
inference(resolution,[status(thm)],[p37,p50]) ).
cnf(p1233,plain,
( member(g(X0,X1,X0),X1)
| union(X0,X1,X0) ),
inference(factoring,[status(thm)],[p282]) ).
cnf(p1234,plain,
( member(g(X0,X1,X0),X2)
| ~ subset(X1,X2)
| union(X0,X1,X0) ),
inference(resolution,[status(thm)],[p1233,c0]) ).
cnf(p2403,plain,
( member(g(X0,cDb,X0),cD_aIb)
| union(X0,cDb,X0) ),
inference(resolution,[status(thm)],[p2386,p1234]) ).
cnf(p2480,plain,
( union(cD_aIb,cDb,cD_aIb)
| union(cD_aIb,cDb,cD_aIb) ),
inference(resolution,[status(thm)],[p2403,p50]) ).
cnf(p2488,plain,
union(cD_aIb,cDb,cD_aIb),
inference(factoring,[status(thm)],[p2480]) ).
cnf(f8,axiom,
( member(Element,Union)
| ~ member(Element,Set2)
| ~ union(Set1,Set2,Union) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_set2_is_member_of_union) ).
fof(f8_nnf,plain,
! [Set1,Set2,Union,Element] :
( member(Element,Union)
| ~ member(Element,Set2)
| ~ union(Set1,Set2,Union) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [Set1,Set2,Union,Element] :
( member(Element,Union)
| ~ member(Element,Set2)
| ~ union(Set1,Set2,Union) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ union(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p2489,plain,
( member(X0,cD_aIb)
| ~ member(X0,cDb) ),
inference(resolution,[status(thm)],[p2488,c8]) ).
cnf(p6747,plain,
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),cD_aIb)
| union(cDa,cDb,cD_aIb) ),
inference(resolution,[status(thm)],[p2365,p2489]) ).
cnf(p9683,plain,
( member(g(cDa,cDb,cD_aIb),cD_aIb)
| union(cDa,cDb,cD_aIb) ),
inference(factoring,[status(thm)],[p6747]) ).
cnf(p69,plain,
( member(X0,c)
| ~ member(X0,cD_aIb) ),
inference(resolution,[status(thm)],[c18,c27]) ).
cnf(p9719,plain,
( member(g(cDa,cDb,cD_aIb),c)
| union(cDa,cDb,cD_aIb) ),
inference(resolution,[status(thm)],[p9683,p69]) ).
cnf(p9728,plain,
( member(g(cDa,cDb,cD_aIb),X0)
| member(g(cDa,cDb,cD_aIb),X1)
| ~ difference(c,X0,X1)
| union(cDa,cDb,cD_aIb) ),
inference(resolution,[status(thm)],[p9719,c20]) ).
cnf(p24318,plain,
( member(g(cDa,cDb,cD_aIb),b)
| member(g(cDa,cDb,cD_aIb),cDb)
| union(cDa,cDb,cD_aIb) ),
inference(resolution,[status(thm)],[p9728,c26]) ).
cnf(f11,axiom,
( union(Set1,Set2,Union)
| ~ member(g(Set1,Set2,Union),Union)
| ~ member(g(Set1,Set2,Union),Set2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_axiom3) ).
fof(f11_nnf,plain,
! [Set1,Set2,Union] :
( union(Set1,Set2,Union)
| ~ member(g(Set1,Set2,Union),Union)
| ~ member(g(Set1,Set2,Union),Set2) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [Set1,Set2,Union] :
( union(Set1,Set2,Union)
| ~ member(g(Set1,Set2,Union),Union)
| ~ member(g(Set1,Set2,Union),Set2) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X2)
| ~ member(g(X0,X1,X2),X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p24331,plain,
( union(cDa,cDb,cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),b)
| union(cDa,cDb,cD_aIb) ),
inference(resolution,[status(thm)],[p24318,c11]) ).
cnf(p37849,plain,
( ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),b)
| union(cDa,cDb,cD_aIb) ),
inference(factoring,[status(thm)],[p24331]) ).
cnf(p37851,plain,
( union(cDa,cDb,cD_aIb)
| member(g(cDa,cDb,cD_aIb),b)
| union(cDa,cDb,cD_aIb) ),
inference(resolution,[status(thm)],[p37849,p9683]) ).
cnf(p37852,plain,
( member(g(cDa,cDb,cD_aIb),b)
| union(cDa,cDb,cD_aIb) ),
inference(factoring,[status(thm)],[p37851]) ).
cnf(f14,axiom,
( member(Element,Intersection)
| ~ member(Element,Set1)
| ~ member(Element,Set2)
| ~ intersection(Set1,Set2,Intersection) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_both_is_member_of_intersection) ).
fof(f14_nnf,plain,
! [Set1,Set2,Intersection,Element] :
( member(Element,Intersection)
| ~ member(Element,Set1)
| ~ member(Element,Set2)
| ~ intersection(Set1,Set2,Intersection) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [Set1,Set2,Intersection,Element] :
( member(Element,Intersection)
| ~ member(Element,Set1)
| ~ member(Element,Set2)
| ~ intersection(Set1,Set2,Intersection) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( member(X3,X2)
| ~ member(X3,X0)
| ~ member(X3,X1)
| ~ intersection(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p62,plain,
( member(X0,aIb)
| ~ member(X0,a)
| ~ member(X0,b) ),
inference(resolution,[status(thm)],[c14,c24]) ).
cnf(p37854,plain,
( member(g(cDa,cDb,cD_aIb),aIb)
| ~ member(g(cDa,cDb,cD_aIb),a)
| union(cDa,cDb,cD_aIb) ),
inference(resolution,[status(thm)],[p37852,p62]) ).
cnf(p24317,plain,
( member(g(cDa,cDb,cD_aIb),a)
| member(g(cDa,cDb,cD_aIb),cDa)
| union(cDa,cDb,cD_aIb) ),
inference(resolution,[status(thm)],[p9728,c25]) ).
cnf(p24320,plain,
( union(cDa,cDb,cD_aIb)
| ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),a)
| union(cDa,cDb,cD_aIb) ),
inference(resolution,[status(thm)],[p24317,c10]) ).
cnf(p37798,plain,
( ~ member(g(cDa,cDb,cD_aIb),cD_aIb)
| member(g(cDa,cDb,cD_aIb),a)
| union(cDa,cDb,cD_aIb) ),
inference(factoring,[status(thm)],[p24320]) ).
cnf(p37800,plain,
( union(cDa,cDb,cD_aIb)
| member(g(cDa,cDb,cD_aIb),a)
| union(cDa,cDb,cD_aIb) ),
inference(resolution,[status(thm)],[p37798,p9683]) ).
cnf(p37803,plain,
( member(g(cDa,cDb,cD_aIb),a)
| union(cDa,cDb,cD_aIb) ),
inference(factoring,[status(thm)],[p37800]) ).
cnf(p37889,plain,
( union(cDa,cDb,cD_aIb)
| member(g(cDa,cDb,cD_aIb),aIb)
| union(cDa,cDb,cD_aIb) ),
inference(resolution,[status(thm)],[p37854,p37803]) ).
cnf(p37890,plain,
( member(g(cDa,cDb,cD_aIb),aIb)
| union(cDa,cDb,cD_aIb) ),
inference(factoring,[status(thm)],[p37889]) ).
cnf(p9720,plain,
( ~ difference(X1,cD_aIb,X0)
| ~ member(g(cDa,cDb,cD_aIb),X0)
| union(cDa,cDb,cD_aIb) ),
inference(resolution,[status(thm)],[p9683,c19]) ).
cnf(p37898,plain,
( ~ difference(X0,cD_aIb,aIb)
| union(cDa,cDb,cD_aIb)
| union(cDa,cDb,cD_aIb) ),
inference(resolution,[status(thm)],[p37890,p9720]) ).
cnf(p37904,plain,
( ~ difference(X0,cD_aIb,aIb)
| union(cDa,cDb,cD_aIb) ),
inference(factoring,[status(thm)],[p37898]) ).
cnf(f23,axiom,
( difference(Set1,Set2,Difference)
| member(k(Set1,Set2,Difference),Set2)
| ~ member(k(Set1,Set2,Difference),Set1)
| ~ member(k(Set1,Set2,Difference),Difference) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_axiom3) ).
fof(f23_nnf,plain,
! [Set1,Set2,Difference] :
( difference(Set1,Set2,Difference)
| member(k(Set1,Set2,Difference),Set2)
| ~ member(k(Set1,Set2,Difference),Set1)
| ~ member(k(Set1,Set2,Difference),Difference) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [Set1,Set2,Difference] :
( difference(Set1,Set2,Difference)
| member(k(Set1,Set2,Difference),Set2)
| ~ member(k(Set1,Set2,Difference),Set1)
| ~ member(k(Set1,Set2,Difference),Difference) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( difference(X0,X1,X2)
| member(k(X0,X1,X2),X1)
| ~ member(k(X0,X1,X2),X0)
| ~ member(k(X0,X1,X2),X2) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p224,plain,
( difference(X0,X1,X0)
| member(k(X0,X1,X0),X1)
| ~ member(k(X0,X1,X0),X0) ),
inference(factoring,[status(thm)],[c23]) ).
cnf(f21,axiom,
( member(k(Set1,Set2,Difference),Difference)
| member(k(Set1,Set2,Difference),Set1)
| difference(Set1,Set2,Difference) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_axiom2) ).
fof(f21_nnf,plain,
! [Set1,Set2,Difference] :
( member(k(Set1,Set2,Difference),Difference)
| member(k(Set1,Set2,Difference),Set1)
| difference(Set1,Set2,Difference) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [Set1,Set2,Difference] :
( member(k(Set1,Set2,Difference),Difference)
| member(k(Set1,Set2,Difference),Set1)
| difference(Set1,Set2,Difference) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( member(k(X0,X1,X2),X2)
| member(k(X0,X1,X2),X0)
| difference(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p168,plain,
( member(k(X0,X1,X0),X0)
| difference(X0,X1,X0) ),
inference(factoring,[status(thm)],[c21]) ).
cnf(p1866,plain,
( difference(X0,X1,X0)
| difference(X0,X1,X0)
| member(k(X0,X1,X0),X1) ),
inference(resolution,[status(thm)],[p224,p168]) ).
cnf(p3760,plain,
( difference(X0,X1,X0)
| member(k(X0,X1,X0),X1) ),
inference(factoring,[status(thm)],[p1866]) ).
cnf(p217,plain,
( ~ difference(X3,X0,X2)
| ~ member(k(X0,X1,X0),X2)
| difference(X0,X1,X0) ),
inference(resolution,[status(thm)],[p168,c19]) ).
cnf(p3772,plain,
( ~ difference(X2,X0,X1)
| difference(X0,X1,X0)
| difference(X0,X1,X0) ),
inference(resolution,[status(thm)],[p3760,p217]) ).
cnf(p3896,plain,
( ~ difference(X2,X0,X1)
| difference(X0,X1,X0) ),
inference(factoring,[status(thm)],[p3772]) ).
cnf(p3899,plain,
difference(aIb,cD_aIb,aIb),
inference(resolution,[status(thm)],[p3896,c27]) ).
cnf(p37905,plain,
union(cDa,cDb,cD_aIb),
inference(resolution,[status(thm)],[p37904,p3899]) ).
cnf(f28,negated_conjecture,
~ union(cDa,cDb,cD_aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cDa_union_cDb_is_cD_aIb) ).
fof(f28_nnf,plain,
~ union(cDa,cDb,cD_aIb),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
~ union(cDa,cDb,cD_aIb),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
~ union(cDa,cDb,cD_aIb),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(p37906,plain,
$false,
inference(resolution,[status(thm)],[p37905,c28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n003.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 09:07:07 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 62.96/43.29 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 62.96/43.29 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------