%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET601+3 : TPTP v9.3.1. Released v2.2.0.
% 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 02:47:30 PM UTC 2026
% Result : Theorem 76.43s 11.40s
% Output : CNFRefutation 76.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 84 ( 24 unt; 0 def)
% Number of atoms : 205 ( 36 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 211 ( 90 ~; 99 |; 18 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 137 ( 0 sgn 132 !; 5 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_union) ).
fof(f3,axiom,
! [X0,X1,X2] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_intersection) ).
fof(f5,axiom,
! [X0,X1,X2] : union(X0,intersection(X1,X2)) = intersection(union(X0,X1),union(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_distributes_over_intersection) ).
fof(f6,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f7,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(f9,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f10,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f13,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f14,conjecture,
! [X0,X1,X2] : union(union(intersection(X0,X1),intersection(X1,X2)),intersection(X2,X0)) = intersection(intersection(union(X0,X1),union(X1,X2)),union(X2,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th72) ).
fof(f15,negated_conjecture,
~ ! [X0,X1,X2] : union(union(intersection(X0,X1),intersection(X1,X2)),intersection(X2,X0)) = intersection(intersection(union(X0,X1),union(X1,X2)),union(X2,X0)),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0,X1,X2] : union(union(intersection(X0,X1),intersection(X1,X2)),intersection(X2,X0)) != intersection(intersection(union(X0,X1),union(X1,X2)),union(X2,X0)),
inference(ennf_transformation,[],[f15]) ).
fof(f18,plain,
union(union(intersection(sK0,sK1),intersection(sK1,sK2)),intersection(sK2,sK0)) != intersection(intersection(union(sK0,sK1),union(sK1,sK2)),union(sK2,sK0)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f16]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) )
& ( ( ~ member(X2,X1)
& ~ member(X2,X0) )
| member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) )
& ( ( ~ member(X2,X1)
& ~ member(X2,X0) )
| member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X2] :
( ( ~ member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X1)
| member(X2,X0) ) ) )
& ( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X1) )
& ( ~ member(X3,X1)
| member(X3,X0) ) ) )
& ( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ) ),
inference(rectify,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X1) )
& ( ~ member(X3,X1)
| member(X3,X0) ) ) )
& ( ( ( member(sK3(X0,X1),X0)
| member(sK3(X0,X1),X1) )
& ( ~ member(sK3(X0,X1),X0)
| ~ member(sK3(X0,X1),X1) ) )
| X0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f22]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( ~ member(X2,intersection(X0,X1))
| ( member(X2,X1)
& member(X2,X0) ) )
& ( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( ~ member(X2,intersection(X0,X1))
| ( member(X2,X1)
& member(X2,X0) ) )
& ( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f27]) ).
fof(f31,plain,
union(union(intersection(sK0,sK1),intersection(sK1,sK2)),intersection(sK2,sK0)) != intersection(intersection(union(sK0,sK1),union(sK1,sK2)),union(sK2,sK0)),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f33,plain,
! [X2,X0,X1] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
inference(cnf_transformation,[],[f3]) ).
fof(f35,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X2,X0,X1] : union(X0,intersection(X1,X2)) = intersection(union(X0,X1),union(X0,X2)),
inference(cnf_transformation,[],[f5]) ).
fof(f41,plain,
! [X2,X0,X1] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
inference(cnf_transformation,[],[f1]) ).
fof(f44,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| member(sK3(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f45,plain,
! [X0,X1] :
( ~ member(sK3(X0,X1),X0)
| ~ member(sK3(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f49,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_49,negated_conjecture,
intersection(intersection(union(sK0,sK1),union(sK1,sK2)),union(sK2,sK0)) != union(union(intersection(sK0,sK1),intersection(sK1,sK2)),intersection(sK2,sK0)),
inference(cnf_transformation,[],[f31]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f32]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
inference(cnf_transformation,[],[f33]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f35]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(union(X0,X1),union(X0,X2)) = union(X0,intersection(X1,X2)),
inference(cnf_transformation,[],[f39]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
inference(cnf_transformation,[],[f41]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(sK3(X0,X1),X1)
| ~ member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( member(sK3(X0,X1),X1)
| member(sK3(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_87,negated_conjecture,
intersection(union(sK0,sK1),intersection(union(sK0,sK2),union(sK1,sK2))) != union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),
inference(theory_normalisation,[status(thm)],[c_49,c_59,c_53,c_51,c_50]) ).
tcf(c_224,plain,
union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))) != intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2))),
inference(ac_demodulation,[status(thm)],[c_87,c_57,c_51,c_50,c_59,c_53]) ).
tcf(c_809,plain,
( ( union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))) = intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2))) )
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2))))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2)))) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_810,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2))))
| member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))))
| ( union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))) = intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2))) ) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_928,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(sK0,sK1))
| member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(intersection(sK0,sK2),intersection(sK1,sK2)))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2)))) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_1054,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(sK0,intersection(sK1,sK2)))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_1055,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(sK1,sK2))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_1129,plain,
! [X0: $i] :
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(X0,union(intersection(sK0,sK2),intersection(sK1,sK2))))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(intersection(sK0,sK2),intersection(sK1,sK2))) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_1135,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(sK1,sK2))
| member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(sK0,sK2))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(intersection(sK0,sK2),intersection(sK1,sK2))) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_2212,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),sK0)
| member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(sK1,sK2))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(sK0,intersection(sK1,sK2))) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_2270,plain,
! [X0: $i] :
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(union(sK1,sK2),X0))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),X0)
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_2278,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),sK2)
| member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),sK1)
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_4865,plain,
! [X0: $i] :
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(intersection(sK0,sK1),X0))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_4870,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),sK1)
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_4871,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),sK0)
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_8499,plain,
! [X0: $i] :
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(sK0,X0))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),sK0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_10539,plain,
! [X0: $i,X1: $i] :
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),X1)
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(X0,X1)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_10540,plain,
! [X0: $i,X1: $i] :
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),X0)
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(X0,X1)) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_20012,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2))))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(sK1,sK2))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(sK0,intersection(sK1,sK2))) ),
inference(instantiation,[status(thm)],[c_2270]) ).
tcf(c_32777,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(sK0,intersection(sK1,sK2)))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),sK0) ),
inference(instantiation,[status(thm)],[c_8499]) ).
tcf(c_38503,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(intersection(sK0,sK2),intersection(sK1,sK2))) ),
inference(instantiation,[status(thm)],[c_1129]) ).
tcf(c_38509,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_4865]) ).
tcf(c_58027,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),sK2)
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(sK0,sK2)) ),
inference(instantiation,[status(thm)],[c_10539]) ).
tcf(c_59218,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),sK1)
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_10540]) ).
tcf(c_61824,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),sK0)
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(sK0,sK2)) ),
inference(instantiation,[status(thm)],[c_10540]) ).
tcf(c_72617,plain,
! [X0: $i] :
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(X0,intersection(sK1,sK2)))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_72620,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(sK0,intersection(sK1,sK2)))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_72617]) ).
tcf(c_73104,plain,
! [X0: $i] :
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(X0,sK2))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),sK2) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_73118,plain,
! [X0: $i] :
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(sK1,X0))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),sK1) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_73493,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(intersection(sK0,sK2),intersection(sK1,sK2)))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_72617]) ).
tcf(c_74371,plain,
! [X0: $i,X1: $i] :
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(X0,X1))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_112086,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(sK1,sK2))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),sK1) ),
inference(instantiation,[status(thm)],[c_73118]) ).
tcf(c_112087,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(sK1,sK2))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),sK2) ),
inference(instantiation,[status(thm)],[c_73104]) ).
tcf(c_137227,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),union(intersection(sK0,sK2),intersection(sK1,sK2)))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(sK0,sK2)) ),
inference(instantiation,[status(thm)],[c_74371]) ).
tcf(c_230730,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(sK0,sK1))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),sK1)
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),sK0) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_231711,plain,
( member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),intersection(sK0,sK2))
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),sK2)
| ~ member(sK3(union(intersection(sK0,sK1),union(intersection(sK0,sK2),intersection(sK1,sK2))),intersection(union(sK1,sK2),union(sK0,intersection(sK1,sK2)))),sK0) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_231712,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_231711,c_230730,c_137227,c_112087,c_112086,c_73493,c_72620,c_61824,c_59218,c_58027,c_38509,c_38503,c_32777,c_20012,c_4870,c_4871,c_2278,c_2212,c_1135,c_1054,c_1055,c_928,c_810,c_809,c_224]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET601+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Thu Sep 24 11:24:17 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 0.08/0.42
% 0.08/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.42
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 76.43/11.40 % SZS status Started for theBenchmark.p
% 76.43/11.40 % SZS status Theorem for theBenchmark.p
% 76.43/11.40
% 76.43/11.40 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 76.43/11.40
% 76.43/11.40 % ------ iProver source info
% 76.43/11.40
% 76.43/11.40 % git: date: 2026-07-19 20:42:38 +0200
% 76.43/11.40 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 76.43/11.40 % git: non_committed_changes: false
% 76.43/11.40
% 76.43/11.40 % ------ Parsing...
% 76.43/11.40 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 76.43/11.40
% 76.43/11.40 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 76.43/11.40
% 76.43/11.40 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 76.43/11.40
% 76.43/11.40 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 76.43/11.40 % ------ Proving...
% 76.43/11.40 % ------ Problem Properties
% 76.43/11.40
% 76.43/11.40 %
% 76.43/11.40 % clauses 21
% 76.43/11.40 % conjectures 0
% 76.43/11.40 % EPR 3
% 76.43/11.40 % Horn 18
% 76.43/11.40 % unary 9
% 76.43/11.40 % binary 6
% 76.43/11.40 % lits 39
% 76.43/11.40 % lits eq 11
% 76.43/11.40 % fd_pure 0
% 76.43/11.40 % fd_pseudo 0
% 76.43/11.40 % fd_cond 0
% 76.43/11.40 % fd_pseudo_cond 3
% 76.43/11.40 % AC symbols 2
% 76.43/11.40
% 76.43/11.40 % ------ Schedule dynamic 5 is on
% 76.43/11.40
% 76.43/11.40 % ------ no conjectures: strip conj schedule
% 76.43/11.40
% 76.43/11.40 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 76.43/11.40
% 76.43/11.40
% 76.43/11.40 % ------
% 76.43/11.40 % Current options:
% 76.43/11.40 % ------
% 76.43/11.40
% 76.43/11.40
% 76.43/11.40 %
% 76.43/11.40
% 76.43/11.40 % ------ Proving...
% 76.43/11.40 % Proof_search_loop: time out after: 9735 full_loop iterations
% 76.43/11.40
% 76.43/11.40 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" stripped conjectures Time Limit: 15.
% 76.43/11.40
% 76.43/11.40
% 76.43/11.40 % ------
% 76.43/11.40 % Current options:
% 76.43/11.40 % ------
% 76.43/11.40
% 76.43/11.40
% 76.43/11.40 %
% 76.43/11.40
% 76.43/11.40 % ------ Proving...
% 76.43/11.40 %
% 76.43/11.40
% 76.43/11.40 % SZS status Theorem for theBenchmark.p
% 76.43/11.40
% 76.43/11.40 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 76.43/11.40
% 76.43/11.40
%------------------------------------------------------------------------------