%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET010+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 : n020.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 02:46:00 PM UTC 2026
% Result : Theorem 6.33s 2.72s
% Output : CNFRefutation 6.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 71 ( 7 unt; 0 def)
% Number of atoms : 209 ( 19 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 238 ( 100 ~; 110 |; 23 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 132 ( 0 sgn 127 !; 5 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f2,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(f3,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f12,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f13,conjecture,
! [X0,X1,X2] : difference(X0,intersection(X1,X2)) = union(difference(X0,X1),difference(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_difference_and_intersection_and_union) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] : difference(X0,intersection(X1,X2)) = union(difference(X0,X1),difference(X0,X2)),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
? [X0,X1,X2] : difference(X0,intersection(X1,X2)) != union(difference(X0,X1),difference(X0,X2)),
inference(ennf_transformation,[],[f14]) ).
fof(f20,plain,
difference(sK0,intersection(sK1,sK2)) != union(difference(sK0,sK1),difference(sK0,sK2)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f15]) ).
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,[],[f12]) ).
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(f26,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,[],[f1]) ).
fof(f27,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,[],[f26]) ).
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(nnf_transformation,[],[f2]) ).
fof(f29,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,[],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( ~ member(X2,difference(X0,X1))
| ( ~ member(X2,X1)
& member(X2,X0) ) )
& ( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( ~ member(X2,difference(X0,X1))
| ( ~ member(X2,X1)
& member(X2,X0) ) )
& ( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f30]) ).
fof(f35,plain,
difference(sK0,intersection(sK1,sK2)) != union(difference(sK0,sK1),difference(sK0,sK2)),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X0,X1] :
( member(sK3(X0,X1),X0)
| member(sK3(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f39,plain,
! [X0,X1] :
( ~ member(sK3(X0,X1),X0)
| ~ member(sK3(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f23]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f51,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f52,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f54,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f56,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_49,negated_conjecture,
union(difference(sK0,sK1),difference(sK0,sK2)) != difference(sK0,intersection(sK1,sK2)),
inference(cnf_transformation,[],[f35]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(sK3(X0,X1),X1)
| ~ member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( member(sK3(X0,X1),X1)
| member(sK3(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_977,plain,
( ( union(difference(sK0,sK1),difference(sK0,sK2)) = difference(sK0,intersection(sK1,sK2)) )
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),difference(sK0,intersection(sK1,sK2)))
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),union(difference(sK0,sK1),difference(sK0,sK2))) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_978,plain,
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),difference(sK0,intersection(sK1,sK2)))
| member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),union(difference(sK0,sK1),difference(sK0,sK2)))
| ( union(difference(sK0,sK1),difference(sK0,sK2)) = difference(sK0,intersection(sK1,sK2)) ) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_1031,plain,
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),difference(sK0,sK2))
| member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),difference(sK0,sK1))
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),union(difference(sK0,sK1),difference(sK0,sK2))) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_1211,plain,
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),sK0)
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),difference(sK0,intersection(sK1,sK2))) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_1345,plain,
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),sK0)
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),difference(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_1640,plain,
! [X0: $i,X1: $i] :
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),X1)
| member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),difference(X0,X1))
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),X0) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_1641,plain,
! [X0: $i,X1: $i] :
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),intersection(X0,X1))
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),X1)
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),X0) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_1642,plain,
! [X0: $i,X1: $i] :
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),union(X1,X0))
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),X0) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_1643,plain,
! [X0: $i,X1: $i] :
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),union(X0,X1))
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),X0) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_1650,plain,
! [X0: $i,X1: $i] :
( ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),X1)
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),difference(X0,X1)) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_1653,plain,
! [X0: $i,X1: $i] :
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),X1)
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),intersection(X0,X1)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_1654,plain,
! [X0: $i,X1: $i] :
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),X0)
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),intersection(X0,X1)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_1658,plain,
! [X0: $i,X1: $i] :
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),X0)
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),difference(X0,X1)) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_4115,plain,
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),union(difference(sK0,sK1),difference(sK0,sK2)))
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),difference(sK0,sK2)) ),
inference(instantiation,[status(thm)],[c_1642]) ).
tcf(c_4182,plain,
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),union(difference(sK0,sK1),difference(sK0,sK2)))
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),difference(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_1643]) ).
tcf(c_4184,plain,
( ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),intersection(sK1,sK2))
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),difference(sK0,intersection(sK1,sK2))) ),
inference(instantiation,[status(thm)],[c_1650]) ).
tcf(c_6960,plain,
! [X0: $i] :
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),intersection(sK1,sK2))
| member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),difference(X0,intersection(sK1,sK2)))
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),X0) ),
inference(instantiation,[status(thm)],[c_1640]) ).
tcf(c_6973,plain,
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),intersection(sK1,sK2))
| member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),difference(sK0,intersection(sK1,sK2)))
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),sK0) ),
inference(instantiation,[status(thm)],[c_6960]) ).
tcf(c_6975,plain,
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),intersection(sK1,sK2))
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),sK2)
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),sK1) ),
inference(instantiation,[status(thm)],[c_1641]) ).
tcf(c_26691,plain,
! [X0: $i] :
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),sK1)
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),intersection(sK1,X0)) ),
inference(instantiation,[status(thm)],[c_1654]) ).
tcf(c_26704,plain,
! [X0: $i] :
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),sK1)
| member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),difference(X0,sK1))
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),X0) ),
inference(instantiation,[status(thm)],[c_1640]) ).
tcf(c_26717,plain,
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),sK1)
| member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),difference(sK0,sK1))
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),sK0) ),
inference(instantiation,[status(thm)],[c_26704]) ).
tcf(c_28175,plain,
( ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),sK2)
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),difference(sK0,sK2)) ),
inference(instantiation,[status(thm)],[c_1650]) ).
tcf(c_39120,plain,
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),sK2)
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),intersection(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_1653]) ).
tcf(c_40840,plain,
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),sK0)
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),difference(sK0,sK2)) ),
inference(instantiation,[status(thm)],[c_1658]) ).
tcf(c_41810,plain,
( ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),sK1)
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),difference(sK0,sK1)) ),
inference(instantiation,[status(thm)],[c_1650]) ).
tcf(c_60549,plain,
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),sK1)
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),intersection(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_26691]) ).
tcf(c_64930,plain,
! [X0: $i] :
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),sK2)
| member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),difference(X0,sK2))
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),X0) ),
inference(instantiation,[status(thm)],[c_1640]) ).
tcf(c_64931,plain,
( member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),sK2)
| member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),difference(sK0,sK2))
| ~ member(sK3(union(difference(sK0,sK1),difference(sK0,sK2)),difference(sK0,intersection(sK1,sK2))),sK0) ),
inference(instantiation,[status(thm)],[c_64930]) ).
tcf(c_64932,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_64931,c_60549,c_41810,c_40840,c_39120,c_28175,c_26717,c_6975,c_6973,c_4184,c_4182,c_4115,c_1345,c_1211,c_1031,c_978,c_977,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET010+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n020.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 09:06:05 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.40 Running first-order theorem proving
% 0.03/0.40 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
% 0.03/0.41
% 0.03/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.41
% 0.03/0.41 % Detected problem language: tptp
% 0.03/0.42 % Proving...
% 6.33/2.72 % SZS status Started for theBenchmark.p
% 6.33/2.72 % SZS status Theorem for theBenchmark.p
% 6.33/2.72
% 6.33/2.72 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.33/2.72
% 6.33/2.72 % ------ iProver source info
% 6.33/2.72
% 6.33/2.72 % git: date: 2026-07-19 20:42:38 +0200
% 6.33/2.72 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.33/2.72 % git: non_committed_changes: false
% 6.33/2.72
% 6.33/2.72 % ------ Parsing...
% 6.33/2.72 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.33/2.72
% 6.33/2.72 % ------ Preprocessing... sup_sim: 0 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 %
% 6.33/2.72
% 6.33/2.72 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.33/2.72
% 6.33/2.72 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.33/2.72 % ------ Proving...
% 6.33/2.72 % ------ Problem Properties
% 6.33/2.72
% 6.33/2.72 %
% 6.33/2.72 % clauses 22
% 6.33/2.72 % conjectures 1
% 6.33/2.72 % EPR 3
% 6.33/2.72 % Horn 18
% 6.33/2.72 % unary 5
% 6.33/2.72 % binary 9
% 6.33/2.72 % lits 47
% 6.33/2.72 % lits eq 6
% 6.33/2.72 % fd_pure 0
% 6.33/2.72 % fd_pseudo 0
% 6.33/2.72 % fd_cond 0
% 6.33/2.72 % fd_pseudo_cond 3
% 6.33/2.72 % AC symbols 0
% 6.33/2.72
% 6.33/2.72 % ------ Schedule dynamic 5 is on
% 6.33/2.72
% 6.33/2.72 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.33/2.72
% 6.33/2.72
% 6.33/2.72 % ------
% 6.33/2.72 % Current options:
% 6.33/2.72 % ------
% 6.33/2.72
% 6.33/2.72
% 6.33/2.72 %
% 6.33/2.72
% 6.33/2.72 % ------ Proving...
% 6.33/2.72 %
% 6.33/2.72
% 6.33/2.72 % SZS status Theorem for theBenchmark.p
% 6.33/2.72
% 6.33/2.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.33/2.72
% 6.33/2.72
%------------------------------------------------------------------------------