%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET007-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n005.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 02:45:59 PM UTC 2026
% Result : Unsatisfiable 4.16s 1.28s
% Output : CNFRefutation 4.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 17
% Syntax : Number of formulae : 93 ( 19 unt; 0 def)
% Number of atoms : 241 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 280 ( 132 ~; 148 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 155 ( 0 sgn 155 !; 0 ?; 115 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-0.ax',membership_in_subsets) ).
fof(f2,axiom,
! [X0,X1] :
( member(member_of_1_not_of_2(X0,X1),X0)
| subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-0.ax',subsets_axiom1) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-0.ax',subsets_axiom2) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( member(X3,X1)
| member(X3,X0)
| ~ member(X3,X2)
| ~ union(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax',member_of_union_is_member_of_one_set) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( member(X3,X2)
| ~ member(X3,X0)
| ~ union(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax',member_of_set1_is_member_of_union) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( member(X3,X2)
| ~ member(X3,X1)
| ~ union(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax',member_of_set2_is_member_of_union) ).
fof(f10,axiom,
! [X2,X0,X1] :
( member(g(X0,X1,X2),X2)
| member(g(X0,X1,X2),X1)
| member(g(X0,X1,X2),X0)
| union(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax',union_axiom1) ).
fof(f11,axiom,
! [X2,X0,X1] :
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X2)
| ~ member(g(X0,X1,X2),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax',union_axiom2) ).
fof(f12,axiom,
! [X2,X0,X1] :
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X2)
| ~ member(g(X0,X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax',union_axiom3) ).
fof(f13,axiom,
! [X2,X3,X0,X1] :
( member(X3,X0)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-2.ax',member_of_intersection_is_member_of_set1) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-2.ax',member_of_intersection_is_member_of_set2) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( member(X3,X2)
| ~ member(X3,X0)
| ~ member(X3,X1)
| ~ intersection(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-2.ax',member_of_both_is_member_of_intersection) ).
fof(f19,axiom,
union(b,c,bUc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_union_c) ).
fof(f20,axiom,
intersection(a,b,aIb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_b) ).
fof(f21,axiom,
intersection(a,c,aIc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_c) ).
fof(f22,axiom,
intersection(a,bUc,aI_bUc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_intersection_bUc) ).
fof(f23,negated_conjecture,
~ union(aIb,aIc,aI_bUc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_aIb_union_aIc_is_aI_bUc) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(member_of_1_not_of_2(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,X1)
| member(X3,X0)
| ~ member(X3,X2)
| ~ union(X0,X1,X2) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,X2)
| ~ member(X3,X0)
| ~ union(X0,X1,X2) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,X2)
| ~ member(X3,X1)
| ~ union(X0,X1,X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( union(X0,X1,X2)
| member(g(X0,X1,X2),X2)
| member(g(X0,X1,X2),X1)
| member(g(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X2)
| ~ member(g(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] :
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X2)
| ~ member(g(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,X0)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,X1)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,X2)
| ~ member(X3,X1)
| ~ member(X3,X0)
| ~ intersection(X0,X1,X2) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_90,plain,
union(b,c,bUc),
inference(cnf_transformation,[],[f19]) ).
tcf(c_91,plain,
intersection(a,b,aIb),
inference(cnf_transformation,[],[f20]) ).
tcf(c_92,plain,
intersection(a,c,aIc),
inference(cnf_transformation,[],[f21]) ).
tcf(c_93,plain,
intersection(a,bUc,aI_bUc),
inference(cnf_transformation,[],[f22]) ).
tcf(c_94,negated_conjecture,
~ union(aIb,aIc,aI_bUc),
inference(cnf_transformation,[],[f23]) ).
tcf(c_411,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| ~ member(g(aIb,aIc,aI_bUc),aIc) ),
inference(resolution,[status(thm)],[c_94,c_83]) ).
tcf(c_418,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| ~ member(g(aIb,aIc,aI_bUc),aIb) ),
inference(resolution,[status(thm)],[c_94,c_82]) ).
tcf(c_425,plain,
( member(g(aIb,aIc,aI_bUc),aI_bUc)
| member(g(aIb,aIc,aI_bUc),aIc)
| member(g(aIb,aIc,aI_bUc),aIb) ),
inference(resolution,[status(thm)],[c_94,c_81]) ).
tcf(c_1409,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( subset(X0_iProver_subset_1,X1_iProver_subset_1)
| ~ member(member_of_1_not_of_2(X0_iProver_subset_1,X1_iProver_subset_1),X1_iProver_subset_1) ),
inference(subtyping,[status(esa)],[c_74]) ).
tcf(c_1410,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( subset(X0_iProver_subset_1,X1_iProver_subset_1)
| member(member_of_1_not_of_2(X0_iProver_subset_1,X1_iProver_subset_1),X0_iProver_subset_1) ),
inference(subtyping,[status(esa)],[c_73]) ).
tcf(c_1411,plain,
! [X0_iProver_member_1: iProver_member_1,X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( member(X0_iProver_member_1,X1_iProver_subset_1)
| ~ subset(X0_iProver_subset_1,X1_iProver_subset_1)
| ~ member(X0_iProver_member_1,X0_iProver_subset_1) ),
inference(subtyping,[status(esa)],[c_72]) ).
tcf(c_1415,plain,
! [X0_iProver_member_1: iProver_member_1,X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1,X2_iProver_subset_1: iProver_subset_1] :
( member(X0_iProver_member_1,X2_iProver_subset_1)
| ~ member(X0_iProver_member_1,X1_iProver_subset_1)
| ~ union(X0_iProver_subset_1,X1_iProver_subset_1,X2_iProver_subset_1) ),
inference(subtyping,[status(esa)],[c_80]) ).
tcf(c_1416,plain,
! [X0_iProver_member_1: iProver_member_1,X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1,X2_iProver_subset_1: iProver_subset_1] :
( member(X0_iProver_member_1,X2_iProver_subset_1)
| ~ member(X0_iProver_member_1,X0_iProver_subset_1)
| ~ union(X0_iProver_subset_1,X1_iProver_subset_1,X2_iProver_subset_1) ),
inference(subtyping,[status(esa)],[c_79]) ).
tcf(c_1417,plain,
! [X0_iProver_member_1: iProver_member_1,X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1,X2_iProver_subset_1: iProver_subset_1] :
( member(X0_iProver_member_1,X1_iProver_subset_1)
| member(X0_iProver_member_1,X0_iProver_subset_1)
| ~ member(X0_iProver_member_1,X2_iProver_subset_1)
| ~ union(X0_iProver_subset_1,X1_iProver_subset_1,X2_iProver_subset_1) ),
inference(subtyping,[status(esa)],[c_78]) ).
tcf(c_1421,plain,
! [X0_iProver_member_1: iProver_member_1,X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1,X2_iProver_subset_1: iProver_subset_1] :
( member(X0_iProver_member_1,X2_iProver_subset_1)
| ~ member(X0_iProver_member_1,X1_iProver_subset_1)
| ~ member(X0_iProver_member_1,X0_iProver_subset_1)
| ~ intersection(X0_iProver_subset_1,X1_iProver_subset_1,X2_iProver_subset_1) ),
inference(subtyping,[status(esa)],[c_86]) ).
tcf(c_1422,plain,
! [X0_iProver_member_1: iProver_member_1,X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1,X2_iProver_subset_1: iProver_subset_1] :
( member(X0_iProver_member_1,X1_iProver_subset_1)
| ~ member(X0_iProver_member_1,X2_iProver_subset_1)
| ~ intersection(X0_iProver_subset_1,X1_iProver_subset_1,X2_iProver_subset_1) ),
inference(subtyping,[status(esa)],[c_85]) ).
tcf(c_1423,plain,
! [X0_iProver_member_1: iProver_member_1,X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1,X2_iProver_subset_1: iProver_subset_1] :
( member(X0_iProver_member_1,X0_iProver_subset_1)
| ~ member(X0_iProver_member_1,X2_iProver_subset_1)
| ~ intersection(X0_iProver_subset_1,X1_iProver_subset_1,X2_iProver_subset_1) ),
inference(subtyping,[status(esa)],[c_84]) ).
tcf(c_1425,plain,
intersection(a,bUc,aI_bUc),
inference(subtyping,[status(esa)],[c_93]) ).
tcf(c_1426,plain,
intersection(a,c,aIc),
inference(subtyping,[status(esa)],[c_92]) ).
tcf(c_1427,plain,
intersection(a,b,aIb),
inference(subtyping,[status(esa)],[c_91]) ).
tcf(c_1428,plain,
union(b,c,bUc),
inference(subtyping,[status(esa)],[c_90]) ).
tcf(c_1436,plain,
! [X0_iProver_subset_1: iProver_subset_1] :
( member(g(aIb,aIc,aI_bUc),X0_iProver_subset_1)
| ~ subset(aIc,X0_iProver_subset_1)
| ~ member(g(aIb,aIc,aI_bUc),aIc) ),
inference(instantiation,[status(thm)],[c_1411]) ).
tcf(c_1437,plain,
( member(g(aIb,aIc,aI_bUc),a)
| ~ subset(aIc,a)
| ~ member(g(aIb,aIc,aI_bUc),aIc) ),
inference(instantiation,[status(thm)],[c_1436]) ).
tcf(c_1440,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( member(g(aIb,aIc,aI_bUc),X1_iProver_subset_1)
| ~ intersection(X0_iProver_subset_1,X1_iProver_subset_1,aIc)
| ~ member(g(aIb,aIc,aI_bUc),aIc) ),
inference(instantiation,[status(thm)],[c_1422]) ).
tcf(c_1446,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1,X2_iProver_subset_1: iProver_subset_1] :
( member(g(aIb,aIc,aI_bUc),X2_iProver_subset_1)
| ~ intersection(X0_iProver_subset_1,X1_iProver_subset_1,X2_iProver_subset_1)
| ~ member(g(aIb,aIc,aI_bUc),X1_iProver_subset_1)
| ~ member(g(aIb,aIc,aI_bUc),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_1421]) ).
tcf(c_1449,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( member(g(aIb,aIc,aI_bUc),X1_iProver_subset_1)
| ~ subset(X0_iProver_subset_1,X1_iProver_subset_1)
| ~ member(g(aIb,aIc,aI_bUc),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_1411]) ).
tcf(c_1451,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1,X2_iProver_subset_1: iProver_subset_1] :
( member(g(aIb,aIc,aI_bUc),X2_iProver_subset_1)
| ~ intersection(X1_iProver_subset_1,X2_iProver_subset_1,X0_iProver_subset_1)
| ~ member(g(aIb,aIc,aI_bUc),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_1422]) ).
tcf(c_1474,plain,
( member(g(aIb,aIc,aI_bUc),c)
| ~ intersection(a,c,aIc)
| ~ member(g(aIb,aIc,aI_bUc),aIc) ),
inference(instantiation,[status(thm)],[c_1440]) ).
tcf(c_1500,plain,
! [X0_iProver_subset_1: iProver_subset_1] :
( member(g(aIb,aIc,aI_bUc),X0_iProver_subset_1)
| ~ subset(aI_bUc,X0_iProver_subset_1)
| ~ member(g(aIb,aIc,aI_bUc),aI_bUc) ),
inference(instantiation,[status(thm)],[c_1449]) ).
tcf(c_1501,plain,
( member(g(aIb,aIc,aI_bUc),a)
| ~ subset(aI_bUc,a)
| ~ member(g(aIb,aIc,aI_bUc),aI_bUc) ),
inference(instantiation,[status(thm)],[c_1500]) ).
tcf(c_1539,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,bUc)
| ~ member(X0_iProver_member_1,aI_bUc) ),
inference(superposition,[status(thm)],[c_1425,c_1422]) ).
tcf(c_1587,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( member(g(aIb,aIc,aI_bUc),X1_iProver_subset_1)
| ~ intersection(X0_iProver_subset_1,X1_iProver_subset_1,aIb)
| ~ member(g(aIb,aIc,aI_bUc),aIb) ),
inference(instantiation,[status(thm)],[c_1451]) ).
tcf(c_1589,plain,
! [X0_iProver_subset_1: iProver_subset_1] :
( member(g(aIb,aIc,aI_bUc),X0_iProver_subset_1)
| ~ subset(aIb,X0_iProver_subset_1)
| ~ member(g(aIb,aIc,aI_bUc),aIb) ),
inference(instantiation,[status(thm)],[c_1449]) ).
tcf(c_1597,plain,
( member(g(aIb,aIc,aI_bUc),a)
| ~ subset(aIb,a)
| ~ member(g(aIb,aIc,aI_bUc),aIb) ),
inference(instantiation,[status(thm)],[c_1589]) ).
tcf(c_1603,plain,
! [X0_iProver_subset_1: iProver_subset_1] :
( subset(aI_bUc,X0_iProver_subset_1)
| member(member_of_1_not_of_2(aI_bUc,X0_iProver_subset_1),bUc) ),
inference(superposition,[status(thm)],[c_1410,c_1539]) ).
tcf(c_1627,plain,
( member(g(aIb,aIc,aI_bUc),b)
| ~ intersection(a,b,aIb)
| ~ member(g(aIb,aIc,aI_bUc),aIb) ),
inference(instantiation,[status(thm)],[c_1587]) ).
tcf(c_1637,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,a)
| ~ member(X0_iProver_member_1,aIb) ),
inference(superposition,[status(thm)],[c_1427,c_1423]) ).
tcf(c_1638,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,a)
| ~ member(X0_iProver_member_1,aIc) ),
inference(superposition,[status(thm)],[c_1426,c_1423]) ).
tcf(c_1639,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,a)
| ~ member(X0_iProver_member_1,aI_bUc) ),
inference(superposition,[status(thm)],[c_1425,c_1423]) ).
tcf(c_1661,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( member(g(aIb,aIc,aI_bUc),aIc)
| ~ intersection(X0_iProver_subset_1,X1_iProver_subset_1,aIc)
| ~ member(g(aIb,aIc,aI_bUc),X1_iProver_subset_1)
| ~ member(g(aIb,aIc,aI_bUc),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_1446]) ).
tcf(c_1700,plain,
! [X0_iProver_member_1: iProver_member_1] :
( member(X0_iProver_member_1,c)
| member(X0_iProver_member_1,b)
| ~ member(X0_iProver_member_1,bUc) ),
inference(superposition,[status(thm)],[c_1428,c_1417]) ).
tcf(c_1790,plain,
! [X0_iProver_subset_1: iProver_subset_1] :
( subset(aIb,X0_iProver_subset_1)
| member(member_of_1_not_of_2(aIb,X0_iProver_subset_1),a) ),
inference(superposition,[status(thm)],[c_1410,c_1637]) ).
tcf(c_1791,plain,
! [X0_iProver_subset_1: iProver_subset_1] :
( subset(aIc,X0_iProver_subset_1)
| member(member_of_1_not_of_2(aIc,X0_iProver_subset_1),a) ),
inference(superposition,[status(thm)],[c_1410,c_1638]) ).
tcf(c_1797,plain,
! [X0_iProver_subset_1: iProver_subset_1] :
( subset(aI_bUc,X0_iProver_subset_1)
| member(member_of_1_not_of_2(aI_bUc,X0_iProver_subset_1),a) ),
inference(superposition,[status(thm)],[c_1410,c_1639]) ).
tcf(c_1799,plain,
subset(aI_bUc,bUc),
inference(superposition,[status(thm)],[c_1603,c_1409]) ).
tcf(c_1819,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( member(g(aIb,aIc,aI_bUc),aIb)
| ~ intersection(X0_iProver_subset_1,X1_iProver_subset_1,aIb)
| ~ member(g(aIb,aIc,aI_bUc),X1_iProver_subset_1)
| ~ member(g(aIb,aIc,aI_bUc),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_1446]) ).
tcf(c_1950,plain,
subset(aIb,a),
inference(superposition,[status(thm)],[c_1790,c_1409]) ).
tcf(c_1970,plain,
subset(aIc,a),
inference(superposition,[status(thm)],[c_1791,c_1409]) ).
tcf(c_1994,plain,
subset(aI_bUc,a),
inference(superposition,[status(thm)],[c_1797,c_1409]) ).
tcf(c_2385,plain,
( member(g(aIb,aIc,aI_bUc),aIc)
| ~ intersection(a,c,aIc)
| ~ member(g(aIb,aIc,aI_bUc),a)
| ~ member(g(aIb,aIc,aI_bUc),c) ),
inference(instantiation,[status(thm)],[c_1661]) ).
tcf(c_2479,plain,
( member(g(aIb,aIc,aI_bUc),aIb)
| ~ intersection(a,b,aIb)
| ~ member(g(aIb,aIc,aI_bUc),a)
| ~ member(g(aIb,aIc,aI_bUc),b) ),
inference(instantiation,[status(thm)],[c_1819]) ).
tcf(c_3319,plain,
! [X0_iProver_subset_1: iProver_subset_1] :
( member(g(aIb,aIc,aI_bUc),X0_iProver_subset_1)
| ~ subset(aI_bUc,X0_iProver_subset_1)
| ~ member(g(aIb,aIc,aI_bUc),aI_bUc) ),
inference(instantiation,[status(thm)],[c_1411]) ).
tcf(c_3326,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1,X2_iProver_subset_1: iProver_subset_1] :
( member(g(aIb,aIc,aI_bUc),X2_iProver_subset_1)
| ~ intersection(X0_iProver_subset_1,X1_iProver_subset_1,X2_iProver_subset_1)
| ~ member(g(aIb,aIc,aI_bUc),X1_iProver_subset_1)
| ~ member(g(aIb,aIc,aI_bUc),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_1421]) ).
tcf(c_3327,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1,X2_iProver_subset_1: iProver_subset_1] :
( member(g(aIb,aIc,aI_bUc),X2_iProver_subset_1)
| ~ union(X1_iProver_subset_1,X0_iProver_subset_1,X2_iProver_subset_1)
| ~ member(g(aIb,aIc,aI_bUc),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_1415]) ).
tcf(c_3328,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1,X2_iProver_subset_1: iProver_subset_1] :
( member(g(aIb,aIc,aI_bUc),X2_iProver_subset_1)
| ~ union(X0_iProver_subset_1,X1_iProver_subset_1,X2_iProver_subset_1)
| ~ member(g(aIb,aIc,aI_bUc),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_1416]) ).
tcf(c_3375,plain,
( member(g(aIb,aIc,aI_bUc),bUc)
| ~ subset(aI_bUc,bUc)
| ~ member(g(aIb,aIc,aI_bUc),aI_bUc) ),
inference(instantiation,[status(thm)],[c_3319]) ).
tcf(c_3451,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( member(g(aIb,aIc,aI_bUc),aI_bUc)
| ~ intersection(X0_iProver_subset_1,X1_iProver_subset_1,aI_bUc)
| ~ member(g(aIb,aIc,aI_bUc),X1_iProver_subset_1)
| ~ member(g(aIb,aIc,aI_bUc),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_3326]) ).
tcf(c_3461,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( member(g(aIb,aIc,aI_bUc),bUc)
| ~ union(X1_iProver_subset_1,X0_iProver_subset_1,bUc)
| ~ member(g(aIb,aIc,aI_bUc),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_3327]) ).
tcf(c_3475,plain,
! [X0_iProver_subset_1: iProver_subset_1,X1_iProver_subset_1: iProver_subset_1] :
( member(g(aIb,aIc,aI_bUc),bUc)
| ~ union(X0_iProver_subset_1,X1_iProver_subset_1,bUc)
| ~ member(g(aIb,aIc,aI_bUc),X0_iProver_subset_1) ),
inference(instantiation,[status(thm)],[c_3328]) ).
tcf(c_3589,plain,
( member(g(aIb,aIc,aI_bUc),c)
| member(g(aIb,aIc,aI_bUc),b)
| ~ member(g(aIb,aIc,aI_bUc),bUc) ),
inference(instantiation,[status(thm)],[c_1700]) ).
tcf(c_3676,plain,
( member(g(aIb,aIc,aI_bUc),aI_bUc)
| ~ intersection(a,bUc,aI_bUc)
| ~ member(g(aIb,aIc,aI_bUc),a)
| ~ member(g(aIb,aIc,aI_bUc),bUc) ),
inference(instantiation,[status(thm)],[c_3451]) ).
tcf(c_3686,plain,
( member(g(aIb,aIc,aI_bUc),bUc)
| ~ union(b,c,bUc)
| ~ member(g(aIb,aIc,aI_bUc),c) ),
inference(instantiation,[status(thm)],[c_3461]) ).
tcf(c_3701,plain,
( member(g(aIb,aIc,aI_bUc),bUc)
| ~ union(b,c,bUc)
| ~ member(g(aIb,aIc,aI_bUc),b) ),
inference(instantiation,[status(thm)],[c_3475]) ).
tcf(c_3705,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3701,c_3686,c_3676,c_3589,c_3375,c_2479,c_2385,c_1994,c_1970,c_1950,c_1799,c_1627,c_1597,c_1501,c_1474,c_1437,c_425,c_418,c_411,c_90,c_91,c_92,c_93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 09:04:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 4.16/1.28 % SZS status Started for theBenchmark.p
% 4.16/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 4.16/1.28
% 4.16/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.16/1.28
% 4.16/1.28 % ------ iProver source info
% 4.16/1.28
% 4.16/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.16/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.16/1.28 % git: non_committed_changes: false
% 4.16/1.28
% 4.16/1.28 % ------ Parsing...% successful
% 4.16/1.28
% 4.16/1.28
% 4.16/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.16/1.28
% 4.16/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.16/1.28
% 4.16/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.16/1.28 % ------ Proving...
% 4.16/1.28 % ------ Problem Properties
% 4.16/1.28
% 4.16/1.28 %
% 4.16/1.28 % clauses 20
% 4.16/1.28 % conjectures 1
% 4.16/1.28 % EPR 12
% 4.16/1.28 % Horn 15
% 4.16/1.28 % unary 5
% 4.16/1.28 % binary 2
% 4.16/1.28 % lits 52
% 4.16/1.28 % lits eq 0
% 4.16/1.28 % fd_pure 0
% 4.16/1.28 % fd_pseudo 0
% 4.16/1.28 % fd_cond 0
% 4.16/1.28 % fd_pseudo_cond 0
% 4.16/1.28 % AC symbols 0
% 4.16/1.28
% 4.16/1.28 % ------ Input Options Time Limit: Unbounded
% 4.16/1.28
% 4.16/1.28
% 4.16/1.28 % ------
% 4.16/1.28 % Current options:
% 4.16/1.28 % ------
% 4.16/1.28
% 4.16/1.28
% 4.16/1.28 %
% 4.16/1.28
% 4.16/1.28 % ------ Proving...
% 4.16/1.28 %
% 4.16/1.28
% 4.16/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 4.16/1.28
% 4.16/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.16/1.28
% 4.16/1.28
%------------------------------------------------------------------------------