%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET007-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 43.88s 6.68s
% Output : Proof 43.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 20
% Syntax : Number of formulae : 169 ( 25 unt; 0 def)
% Number of atoms : 431 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 408 ( 146 ~; 262 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 265 ( 8 sgn 98 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f15,axiom,
( member(h(Set1,Set2,Intersection),Set1)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_axiom1) ).
fof(f15_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)],[f15]) ).
fof(f15_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)],[f15_nnf]) ).
cnf(c15,plain,
( member(h(X0,X1,X2),X0)
| intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2) ),
inference(cnf_transformation,[status(esa)],[f15_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(p103,plain,
( member(h(X0,X1,X2),X3)
| ~ subset(X2,X3)
| member(h(X0,X1,X2),X0)
| intersection(X0,X1,X2) ),
inference(resolution,[status(thm)],[c15,c0]) ).
cnf(p911,plain,
( ~ subset(X2,X0)
| member(h(X0,X1,X2),X0)
| intersection(X0,X1,X2) ),
inference(factoring,[status(thm)],[p103]) ).
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(f20,axiom,
intersection(a,c,aIc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_intersection_c) ).
fof(f20_nnf,plain,
intersection(a,c,aIc),
inference(nnf_transformation,[status(thm)],[f20]) ).
cnf(c20,plain,
intersection(a,c,aIc),
inference(cnf_transformation,[status(esa)],[f20_nnf]) ).
cnf(p79,plain,
( member(X0,c)
| ~ member(X0,aIc) ),
inference(resolution,[status(thm)],[c13,c20]) ).
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(p86,plain,
( subset(aIc,X0)
| member(member_of_1_not_of_2(aIc,X0),c) ),
inference(resolution,[status(thm)],[p79,c1]) ).
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(p157,plain,
( subset(aIc,c)
| subset(aIc,c) ),
inference(resolution,[status(thm)],[p86,c2]) ).
cnf(p159,plain,
subset(aIc,c),
inference(factoring,[status(thm)],[p157]) ).
cnf(p1039,plain,
( member(h(c,X0,aIc),c)
| intersection(c,X0,aIc) ),
inference(resolution,[status(thm)],[p911,p159]) ).
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(p96,plain,
( member(X0,aIc)
| ~ member(X0,a)
| ~ member(X0,c) ),
inference(resolution,[status(thm)],[c14,c20]) ).
cnf(p1083,plain,
( member(h(c,X0,aIc),aIc)
| ~ member(h(c,X0,aIc),a)
| intersection(c,X0,aIc) ),
inference(resolution,[status(thm)],[p1039,p96]) ).
cnf(f16,axiom,
( member(h(Set1,Set2,Intersection),Set2)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Intersection) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_axiom2) ).
fof(f16_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)],[f16]) ).
fof(f16_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)],[f16_nnf]) ).
cnf(c16,plain,
( member(h(X0,X1,X2),X1)
| intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p128,plain,
( member(h(X0,X1,X2),X3)
| ~ subset(X2,X3)
| member(h(X0,X1,X2),X1)
| intersection(X0,X1,X2) ),
inference(resolution,[status(thm)],[c16,c0]) ).
cnf(p1240,plain,
( ~ subset(X2,X1)
| member(h(X0,X1,X2),X1)
| intersection(X0,X1,X2) ),
inference(factoring,[status(thm)],[p128]) ).
cnf(f21,axiom,
intersection(a,bUc,aI_bUc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_intersection_bUc) ).
fof(f21_nnf,plain,
intersection(a,bUc,aI_bUc),
inference(nnf_transformation,[status(thm)],[f21]) ).
cnf(c21,plain,
intersection(a,bUc,aI_bUc),
inference(cnf_transformation,[status(esa)],[f21_nnf]) ).
cnf(p97,plain,
( member(X0,aI_bUc)
| ~ member(X0,a)
| ~ member(X0,bUc) ),
inference(resolution,[status(thm)],[c14,c21]) ).
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(f18,axiom,
union(b,c,bUc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_union_c) ).
fof(f18_nnf,plain,
union(b,c,bUc),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
union(b,c,bUc),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(p33,plain,
( member(X0,bUc)
| ~ member(X0,c) ),
inference(resolution,[status(thm)],[c8,c18]) ).
cnf(p158,plain,
( member(member_of_1_not_of_2(aIc,X0),bUc)
| subset(aIc,X0) ),
inference(resolution,[status(thm)],[p86,p33]) ).
cnf(p229,plain,
( subset(aIc,X0)
| member(member_of_1_not_of_2(aIc,X0),aI_bUc)
| ~ member(member_of_1_not_of_2(aIc,X0),a) ),
inference(resolution,[status(thm)],[p97,p158]) ).
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(p60,plain,
( member(X0,a)
| ~ member(X0,aIc) ),
inference(resolution,[status(thm)],[c12,c20]) ).
cnf(p67,plain,
( subset(aIc,X0)
| member(member_of_1_not_of_2(aIc,X0),a) ),
inference(resolution,[status(thm)],[p60,c1]) ).
cnf(p547,plain,
( subset(aIc,X0)
| subset(aIc,X0)
| member(member_of_1_not_of_2(aIc,X0),aI_bUc) ),
inference(resolution,[status(thm)],[p229,p67]) ).
cnf(p566,plain,
( subset(aIc,X0)
| member(member_of_1_not_of_2(aIc,X0),aI_bUc) ),
inference(factoring,[status(thm)],[p547]) ).
cnf(p568,plain,
( subset(aIc,aI_bUc)
| subset(aIc,aI_bUc) ),
inference(resolution,[status(thm)],[p566,c2]) ).
cnf(p569,plain,
subset(aIc,aI_bUc),
inference(factoring,[status(thm)],[p568]) ).
cnf(p1279,plain,
( member(h(X0,aI_bUc,aIc),aI_bUc)
| intersection(X0,aI_bUc,aIc) ),
inference(resolution,[status(thm)],[p1240,p569]) ).
cnf(p61,plain,
( member(X0,a)
| ~ member(X0,aI_bUc) ),
inference(resolution,[status(thm)],[c12,c21]) ).
cnf(p1348,plain,
( member(h(X0,aI_bUc,aIc),a)
| intersection(X0,aI_bUc,aIc) ),
inference(resolution,[status(thm)],[p1279,p61]) ).
cnf(p2885,plain,
( intersection(c,aI_bUc,aIc)
| member(h(c,aI_bUc,aIc),aIc)
| intersection(c,aI_bUc,aIc) ),
inference(resolution,[status(thm)],[p1083,p1348]) ).
cnf(p2900,plain,
( member(h(c,aI_bUc,aIc),aIc)
| intersection(c,aI_bUc,aIc) ),
inference(factoring,[status(thm)],[p2885]) ).
cnf(f17,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/sandbox/benchmark/theBenchmark.p',intersection_axiom3) ).
fof(f17_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)],[f17]) ).
fof(f17_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)],[f17_nnf]) ).
cnf(c17,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)],[f17_sk]) ).
cnf(p2902,plain,
( intersection(c,aI_bUc,aIc)
| ~ member(h(c,aI_bUc,aIc),c)
| ~ member(h(c,aI_bUc,aIc),aI_bUc)
| intersection(c,aI_bUc,aIc) ),
inference(resolution,[status(thm)],[p2900,c17]) ).
cnf(p6632,plain,
( ~ member(h(c,aI_bUc,aIc),c)
| ~ member(h(c,aI_bUc,aIc),aI_bUc)
| intersection(c,aI_bUc,aIc) ),
inference(factoring,[status(thm)],[p2902]) ).
cnf(p6658,plain,
( intersection(c,aI_bUc,aIc)
| ~ member(h(c,aI_bUc,aIc),c)
| intersection(c,aI_bUc,aIc) ),
inference(resolution,[status(thm)],[p6632,p1279]) ).
cnf(p6659,plain,
( ~ member(h(c,aI_bUc,aIc),c)
| intersection(c,aI_bUc,aIc) ),
inference(factoring,[status(thm)],[p6658]) ).
cnf(p6660,plain,
( intersection(c,aI_bUc,aIc)
| intersection(c,aI_bUc,aIc) ),
inference(resolution,[status(thm)],[p6659,p1039]) ).
cnf(p6661,plain,
intersection(c,aI_bUc,aIc),
inference(factoring,[status(thm)],[p6660]) ).
cnf(p6664,plain,
( member(X0,aIc)
| ~ member(X0,c)
| ~ member(X0,aI_bUc) ),
inference(resolution,[status(thm)],[p6661,c14]) ).
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(p42,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)],[p42]) ).
cnf(f19,axiom,
intersection(a,b,aIb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_intersection_b) ).
fof(f19_nnf,plain,
intersection(a,b,aIb),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
intersection(a,b,aIb),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(p78,plain,
( member(X0,b)
| ~ member(X0,aIb) ),
inference(resolution,[status(thm)],[c13,c19]) ).
cnf(p82,plain,
( subset(aIb,X0)
| member(member_of_1_not_of_2(aIb,X0),b) ),
inference(resolution,[status(thm)],[p78,c1]) ).
cnf(f7,axiom,
( member(Element,Union)
| ~ member(Element,Set1)
| ~ union(Set1,Set2,Union) ),
file('/export/starexec/sandbox/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(p31,plain,
( member(X0,bUc)
| ~ member(X0,b) ),
inference(resolution,[status(thm)],[c7,c18]) ).
cnf(p150,plain,
( member(member_of_1_not_of_2(aIb,X0),bUc)
| subset(aIb,X0) ),
inference(resolution,[status(thm)],[p82,p31]) ).
cnf(p228,plain,
( subset(aIb,X0)
| member(member_of_1_not_of_2(aIb,X0),aI_bUc)
| ~ member(member_of_1_not_of_2(aIb,X0),a) ),
inference(resolution,[status(thm)],[p97,p150]) ).
cnf(p59,plain,
( member(X0,a)
| ~ member(X0,aIb) ),
inference(resolution,[status(thm)],[c12,c19]) ).
cnf(p62,plain,
( subset(aIb,X0)
| member(member_of_1_not_of_2(aIb,X0),a) ),
inference(resolution,[status(thm)],[p59,c1]) ).
cnf(p520,plain,
( subset(aIb,X0)
| subset(aIb,X0)
| member(member_of_1_not_of_2(aIb,X0),aI_bUc) ),
inference(resolution,[status(thm)],[p228,p62]) ).
cnf(p521,plain,
( subset(aIb,X0)
| member(member_of_1_not_of_2(aIb,X0),aI_bUc) ),
inference(factoring,[status(thm)],[p520]) ).
cnf(p523,plain,
( subset(aIb,aI_bUc)
| subset(aIb,aI_bUc) ),
inference(resolution,[status(thm)],[p521,c2]) ).
cnf(p524,plain,
subset(aIb,aI_bUc),
inference(factoring,[status(thm)],[p523]) ).
cnf(p1963,plain,
( member(g(aIb,X0,aI_bUc),aI_bUc)
| member(g(aIb,X0,aI_bUc),X0)
| union(aIb,X0,aI_bUc) ),
inference(resolution,[status(thm)],[p337,p524]) ).
cnf(p40,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(p58,plain,
( union(X0,X1,X0)
| ~ member(g(X0,X1,X0),X0) ),
inference(factoring,[status(thm)],[c10]) ).
cnf(p280,plain,
( union(X0,X1,X0)
| member(g(X0,X1,X0),X1)
| union(X0,X1,X0) ),
inference(resolution,[status(thm)],[p40,p58]) ).
cnf(p697,plain,
( member(g(X0,X1,X0),X1)
| union(X0,X1,X0) ),
inference(factoring,[status(thm)],[p280]) ).
cnf(p698,plain,
( member(g(X0,X1,X0),X2)
| ~ subset(X1,X2)
| union(X0,X1,X0) ),
inference(resolution,[status(thm)],[p697,c0]) ).
cnf(p910,plain,
( member(g(X0,aIc,X0),aI_bUc)
| union(X0,aIc,X0) ),
inference(resolution,[status(thm)],[p698,p569]) ).
cnf(p958,plain,
( union(aI_bUc,aIc,aI_bUc)
| union(aI_bUc,aIc,aI_bUc) ),
inference(resolution,[status(thm)],[p910,p58]) ).
cnf(p959,plain,
union(aI_bUc,aIc,aI_bUc),
inference(factoring,[status(thm)],[p958]) ).
cnf(p960,plain,
( member(X0,aI_bUc)
| ~ member(X0,aIc) ),
inference(resolution,[status(thm)],[p959,c8]) ).
cnf(p3578,plain,
( member(g(aIb,aIc,aI_bUc),aI_bUc)
| member(g(aIb,aIc,aI_bUc),aI_bUc)
| union(aIb,aIc,aI_bUc) ),
inference(resolution,[status(thm)],[p1963,p960]) ).
cnf(p5028,plain,
( member(g(aIb,aIc,aI_bUc),aI_bUc)
| union(aIb,aIc,aI_bUc) ),
inference(factoring,[status(thm)],[p3578]) ).
cnf(p6750,plain,
( union(aIb,aIc,aI_bUc)
| member(g(aIb,aIc,aI_bUc),aIc)
| ~ member(g(aIb,aIc,aI_bUc),c) ),
inference(resolution,[status(thm)],[p6664,p5028]) ).
cnf(p80,plain,
( member(X0,bUc)
| ~ member(X0,aI_bUc) ),
inference(resolution,[status(thm)],[c13,c21]) ).
cnf(p5031,plain,
( member(g(aIb,aIc,aI_bUc),bUc)
| union(aIb,aIc,aI_bUc) ),
inference(resolution,[status(thm)],[p5028,p80]) ).
cnf(f6,axiom,
( member(Element,Set2)
| member(Element,Set1)
| ~ member(Element,Union)
| ~ union(Set1,Set2,Union) ),
file('/export/starexec/sandbox/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(p29,plain,
( member(X0,c)
| member(X0,b)
| ~ member(X0,bUc) ),
inference(resolution,[status(thm)],[c6,c18]) ).
cnf(p5034,plain,
( member(g(aIb,aIc,aI_bUc),c)
| member(g(aIb,aIc,aI_bUc),b)
| union(aIb,aIc,aI_bUc) ),
inference(resolution,[status(thm)],[p5031,p29]) ).
cnf(p6796,plain,
( member(g(aIb,aIc,aI_bUc),b)
| union(aIb,aIc,aI_bUc)
| union(aIb,aIc,aI_bUc)
| member(g(aIb,aIc,aI_bUc),aIc) ),
inference(resolution,[status(thm)],[p6750,p5034]) ).
cnf(p7810,plain,
( member(g(aIb,aIc,aI_bUc),b)
| union(aIb,aIc,aI_bUc)
| member(g(aIb,aIc,aI_bUc),aIc) ),
inference(factoring,[status(thm)],[p6796]) ).
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(p7812,plain,
( union(aIb,aIc,aI_bUc)
| ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| member(g(aIb,aIc,aI_bUc),b)
| union(aIb,aIc,aI_bUc) ),
inference(resolution,[status(thm)],[p7810,c11]) ).
cnf(p7890,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| member(g(aIb,aIc,aI_bUc),b)
| union(aIb,aIc,aI_bUc) ),
inference(factoring,[status(thm)],[p7812]) ).
cnf(p7892,plain,
( union(aIb,aIc,aI_bUc)
| member(g(aIb,aIc,aI_bUc),b)
| union(aIb,aIc,aI_bUc) ),
inference(resolution,[status(thm)],[p7890,p5028]) ).
cnf(p7893,plain,
( member(g(aIb,aIc,aI_bUc),b)
| union(aIb,aIc,aI_bUc) ),
inference(factoring,[status(thm)],[p7892]) ).
cnf(p149,plain,
( subset(aIb,b)
| subset(aIb,b) ),
inference(resolution,[status(thm)],[p82,c2]) ).
cnf(p151,plain,
subset(aIb,b),
inference(factoring,[status(thm)],[p149]) ).
cnf(p1038,plain,
( member(h(b,X0,aIb),b)
| intersection(b,X0,aIb) ),
inference(resolution,[status(thm)],[p911,p151]) ).
cnf(p95,plain,
( member(X0,aIb)
| ~ member(X0,a)
| ~ member(X0,b) ),
inference(resolution,[status(thm)],[c14,c19]) ).
cnf(p1080,plain,
( member(h(b,X0,aIb),aIb)
| ~ member(h(b,X0,aIb),a)
| intersection(b,X0,aIb) ),
inference(resolution,[status(thm)],[p1038,p95]) ).
cnf(p1278,plain,
( member(h(X0,aI_bUc,aIb),aI_bUc)
| intersection(X0,aI_bUc,aIb) ),
inference(resolution,[status(thm)],[p1240,p524]) ).
cnf(p1345,plain,
( member(h(X0,aI_bUc,aIb),a)
| intersection(X0,aI_bUc,aIb) ),
inference(resolution,[status(thm)],[p1278,p61]) ).
cnf(p2862,plain,
( intersection(b,aI_bUc,aIb)
| member(h(b,aI_bUc,aIb),aIb)
| intersection(b,aI_bUc,aIb) ),
inference(resolution,[status(thm)],[p1080,p1345]) ).
cnf(p2875,plain,
( member(h(b,aI_bUc,aIb),aIb)
| intersection(b,aI_bUc,aIb) ),
inference(factoring,[status(thm)],[p2862]) ).
cnf(p2883,plain,
( intersection(b,aI_bUc,aIb)
| ~ member(h(b,aI_bUc,aIb),b)
| ~ member(h(b,aI_bUc,aIb),aI_bUc)
| intersection(b,aI_bUc,aIb) ),
inference(resolution,[status(thm)],[p2875,c17]) ).
cnf(p6529,plain,
( ~ member(h(b,aI_bUc,aIb),b)
| ~ member(h(b,aI_bUc,aIb),aI_bUc)
| intersection(b,aI_bUc,aIb) ),
inference(factoring,[status(thm)],[p2883]) ).
cnf(p6530,plain,
( intersection(b,aI_bUc,aIb)
| ~ member(h(b,aI_bUc,aIb),b)
| intersection(b,aI_bUc,aIb) ),
inference(resolution,[status(thm)],[p6529,p1278]) ).
cnf(p6531,plain,
( ~ member(h(b,aI_bUc,aIb),b)
| intersection(b,aI_bUc,aIb) ),
inference(factoring,[status(thm)],[p6530]) ).
cnf(p6532,plain,
( intersection(b,aI_bUc,aIb)
| intersection(b,aI_bUc,aIb) ),
inference(resolution,[status(thm)],[p6531,p1038]) ).
cnf(p6536,plain,
intersection(b,aI_bUc,aIb),
inference(factoring,[status(thm)],[p6532]) ).
cnf(p6537,plain,
( member(X0,aIb)
| ~ member(X0,b)
| ~ member(X0,aI_bUc) ),
inference(resolution,[status(thm)],[p6536,c14]) ).
cnf(p6624,plain,
( union(aIb,aIc,aI_bUc)
| member(g(aIb,aIc,aI_bUc),aIb)
| ~ member(g(aIb,aIc,aI_bUc),b) ),
inference(resolution,[status(thm)],[p6537,p5028]) ).
cnf(p7896,plain,
( union(aIb,aIc,aI_bUc)
| member(g(aIb,aIc,aI_bUc),aIb)
| union(aIb,aIc,aI_bUc) ),
inference(resolution,[status(thm)],[p7893,p6624]) ).
cnf(p7897,plain,
( member(g(aIb,aIc,aI_bUc),aIb)
| union(aIb,aIc,aI_bUc) ),
inference(factoring,[status(thm)],[p7896]) ).
cnf(p7899,plain,
( union(aIb,aIc,aI_bUc)
| ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| union(aIb,aIc,aI_bUc) ),
inference(resolution,[status(thm)],[p7897,c10]) ).
cnf(p7900,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| union(aIb,aIc,aI_bUc) ),
inference(factoring,[status(thm)],[p7899]) ).
cnf(p7902,plain,
( union(aIb,aIc,aI_bUc)
| union(aIb,aIc,aI_bUc) ),
inference(resolution,[status(thm)],[p7900,p5028]) ).
cnf(p7903,plain,
union(aIb,aIc,aI_bUc),
inference(factoring,[status(thm)],[p7902]) ).
cnf(f22,negated_conjecture,
~ union(aIb,aIc,aI_bUc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_aIb_union_aIc_is_aI_bUc) ).
fof(f22_nnf,plain,
~ union(aIb,aIc,aI_bUc),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
~ union(aIb,aIc,aI_bUc),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
~ union(aIb,aIc,aI_bUc),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(p7904,plain,
$false,
inference(resolution,[status(thm)],[p7903,c22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n002.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 09:07:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 43.88/6.68 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.88/6.68 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------