%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET613+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.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 02:47:34 PM UTC 2026
% Result : Theorem 16.71s 8.01s
% Output : CNFRefutation 16.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 85 ( 9 unt; 0 def)
% Number of atoms : 223 ( 16 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 239 ( 101 ~; 116 |; 16 &)
% ( 4 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 125 ( 0 sgn 121 !; 4 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
<=> member(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_equal) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f3,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f4,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f11,conjecture,
! [X0,X1] : difference(union(X0,X1),intersection(X0,X1)) = union(difference(X0,X1),difference(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_difference_union_intersection) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] : difference(union(X0,X1),intersection(X0,X1)) = union(difference(X0,X1),difference(X1,X0)),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ? [X2] :
( member(X2,X0)
<~> member(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f1]) ).
fof(f15,plain,
? [X0,X1] : difference(union(X0,X1),intersection(X0,X1)) != union(difference(X0,X1),difference(X1,X0)),
inference(ennf_transformation,[],[f12]) ).
fof(f16,plain,
! [X0,X1] :
( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( ( ( member(sK0(X0,X1),X0)
| member(sK0(X0,X1),X1) )
& ( ~ member(sK0(X0,X1),X0)
| ~ member(sK0(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f16]) ).
fof(f18,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,[],[f2]) ).
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(flattening,[],[f18]) ).
fof(f20,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,[],[f3]) ).
fof(f21,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,[],[f20]) ).
fof(f22,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,[],[f4]) ).
fof(f23,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,[],[f22]) ).
fof(f32,plain,
difference(union(sK3,sK4),intersection(sK3,sK4)) != union(difference(sK3,sK4),difference(sK4,sK3)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f15]) ).
fof(f33,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| member(sK0(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f34,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X0)
| ~ member(sK0(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f17]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f21]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f43,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f57,plain,
difference(union(sK3,sK4),intersection(sK3,sK4)) != union(difference(sK3,sK4),difference(sK4,sK3)),
inference(cnf_transformation,[],[f32]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(sK0(X0,X1),X1)
| ~ member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X1)
| member(sK0(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_71,negated_conjecture,
union(difference(sK3,sK4),difference(sK4,sK3)) != difference(union(sK3,sK4),intersection(sK3,sK4)),
inference(cnf_transformation,[],[f57]) ).
tcf(c_556,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(union(sK3,sK4),intersection(sK3,sK4)))
| member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK3,sK4),difference(sK4,sK3)))
| ( union(difference(sK3,sK4),difference(sK4,sK3)) = difference(union(sK3,sK4),intersection(sK3,sK4)) ) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_580,plain,
( ( union(difference(sK3,sK4),difference(sK4,sK3)) = difference(union(sK3,sK4),intersection(sK3,sK4)) )
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(union(sK3,sK4),intersection(sK3,sK4)))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK3,sK4),difference(sK4,sK3))) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_593,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(sK4,sK3))
| member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(sK3,sK4))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK3,sK4),difference(sK4,sK3))) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_696,plain,
( ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),intersection(sK3,sK4))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(union(sK3,sK4),intersection(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_697,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(sK3,sK4))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(union(sK3,sK4),intersection(sK3,sK4))) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_988,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4)
| member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK3)
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_1022,plain,
( ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4)
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_1023,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK3)
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_1206,plain,
( ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK3)
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(sK4,sK3)) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_1207,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4)
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(sK4,sK3)) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_5016,plain,
! [X0: $i,X1: $i] :
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),intersection(X0,X1))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),X1)
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),X0) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_5017,plain,
! [X0: $i,X1: $i] :
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),X1)
| member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(X0,X1))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),X0) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_5019,plain,
! [X0: $i,X1: $i] :
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(X0,X1))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_5020,plain,
! [X0: $i,X1: $i] :
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(X1,X0))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),X0) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_5057,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4)
| member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK3)
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_5058,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4)
| member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_5057,c_71,c_556,c_593,c_697,c_988,c_1023,c_1207]) ).
tcf(c_5352,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),intersection(sK3,sK4))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4)
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK3) ),
inference(instantiation,[status(thm)],[c_5016]) ).
tcf(c_5353,plain,
( ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK3)
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4) ),
inference(global_subsumption_just,[status(thm)],[c_5352,c_71,c_556,c_593,c_696,c_1022,c_1206,c_5352]) ).
tcf(c_5354,plain,
( ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4)
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK3) ),
inference(renaming,[status(thm)],[c_5353]) ).
tcf(c_5360,plain,
! [X0: $i,X1: $i] :
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),X0)
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),intersection(X0,X1)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_5361,plain,
! [X0: $i,X1: $i] :
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),X1)
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),intersection(X0,X1)) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_5363,plain,
! [X0: $i] :
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),intersection(sK3,sK4))
| member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(X0,intersection(sK3,sK4)))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),X0) ),
inference(instantiation,[status(thm)],[c_5017]) ).
tcf(c_5365,plain,
! [X0: $i] :
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK3,sK4),difference(sK4,sK3)))
| member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(X0,union(difference(sK3,sK4),difference(sK4,sK3))))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),X0) ),
inference(instantiation,[status(thm)],[c_5017]) ).
tcf(c_5389,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK3,sK4),difference(sK4,sK3)))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_5019]) ).
tcf(c_5397,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK3,sK4),difference(sK4,sK3)))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(sK4,sK3)) ),
inference(instantiation,[status(thm)],[c_5020]) ).
tcf(c_6422,plain,
! [X0: $i] :
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(X0,sK4))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4) ),
inference(instantiation,[status(thm)],[c_5020]) ).
tcf(c_6425,plain,
! [X0: $i] :
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),X0)
| member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(sK4,X0))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4) ),
inference(instantiation,[status(thm)],[c_5017]) ).
tcf(c_6426,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK3)
| member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(sK4,sK3))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4) ),
inference(instantiation,[status(thm)],[c_6425]) ).
tcf(c_6429,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(sK3,sK4))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4) ),
inference(instantiation,[status(thm)],[c_6422]) ).
tcf(c_6443,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),intersection(sK3,sK4))
| member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(union(sK3,sK4),intersection(sK3,sK4)))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_5363]) ).
tcf(c_6444,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),intersection(sK3,sK4))
| member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(sK4,intersection(sK3,sK4)))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4) ),
inference(instantiation,[status(thm)],[c_5363]) ).
tcf(c_6445,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),intersection(sK3,sK4))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4) ),
inference(global_subsumption_just,[status(thm)],[c_6444,c_71,c_580,c_5354,c_5397,c_6426,c_6429,c_6443]) ).
tcf(c_6453,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK3,sK4),difference(sK4,sK3)))
| member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(sK4,union(difference(sK3,sK4),difference(sK4,sK3))))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4) ),
inference(instantiation,[status(thm)],[c_5365]) ).
tcf(c_6454,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK3,sK4),difference(sK4,sK3)))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4) ),
inference(global_subsumption_just,[status(thm)],[c_6453,c_5354,c_5397,c_6426]) ).
tcf(c_6596,plain,
! [X0: $i] :
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4)
| member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(X0,sK4))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),X0) ),
inference(instantiation,[status(thm)],[c_5017]) ).
tcf(c_6597,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4)
| member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),difference(sK3,sK4))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK3) ),
inference(instantiation,[status(thm)],[c_6596]) ).
tcf(c_6631,plain,
! [X0: $i] :
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK3,sK4),difference(sK4,sK3)))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),intersection(union(difference(sK3,sK4),difference(sK4,sK3)),X0)) ),
inference(instantiation,[status(thm)],[c_5360]) ).
tcf(c_6633,plain,
member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(difference(sK3,sK4),difference(sK4,sK3))),
inference(global_subsumption_just,[status(thm)],[c_6631,c_5058,c_5389,c_6454,c_6597]) ).
tcf(c_6667,plain,
! [X0: $i] :
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4)
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),intersection(X0,sK4)) ),
inference(instantiation,[status(thm)],[c_5361]) ).
tcf(c_6668,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK4)
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_6667]) ).
tcf(c_6926,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK3)
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_5360]) ).
tcf(c_6927,plain,
member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK3),
inference(global_subsumption_just,[status(thm)],[c_6926,c_5058,c_6445,c_6926]) ).
tcf(c_14504,plain,
( member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),union(sK3,sK4))
| ~ member(sK0(union(difference(sK3,sK4),difference(sK4,sK3)),difference(union(sK3,sK4),intersection(sK3,sK4))),sK3) ),
inference(instantiation,[status(thm)],[c_5019]) ).
tcf(c_14505,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_14504,c_6927,c_6668,c_6633,c_6443,c_5354,c_580,c_71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET613+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/5.31 % Computer : n012.cluster.edu
% 0.04/5.31 % Model : x86_64 x86_64
% 0.04/5.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/5.31 % Memory : 8046.5625MB
% 0.04/5.31 % OS : Linux 6.8.0-71-generic
% 0.04/5.31 % CPULimit : 300
% 0.04/5.31 % WCLimit : 300
% 0.04/5.31 % DateTime : Thu Sep 24 11:27:26 UTC 2026
% 0.04/5.31 % CPUTime :
% 0.04/5.31 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/5.33 Running first-order theorem proving
% 0.04/5.33 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/5.34
% 0.04/5.34 % ======== iProver multi-core TPTP/SMT =========
% 0.04/5.34
% 0.04/5.34 % Detected problem language: tptp
% 0.04/5.35 % Proving...
% 16.71/8.01 % SZS status Started for theBenchmark.p
% 16.71/8.01 % SZS status Theorem for theBenchmark.p
% 16.71/8.01
% 16.71/8.01 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 16.71/8.01
% 16.71/8.01 % ------ iProver source info
% 16.71/8.01
% 16.71/8.01 % git: date: 2026-07-19 20:42:38 +0200
% 16.71/8.01 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 16.71/8.01 % git: non_committed_changes: false
% 16.71/8.01
% 16.71/8.01 % ------ Parsing...
% 16.71/8.01 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 16.71/8.01
% 16.71/8.01 % ------ 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 %
% 16.71/8.01
% 16.71/8.01 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 16.71/8.01
% 16.71/8.01 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 16.71/8.01 % ------ Proving...
% 16.71/8.01 % ------ Problem Properties
% 16.71/8.01
% 16.71/8.01 %
% 16.71/8.01 % clauses 21
% 16.71/8.01 % conjectures 1
% 16.71/8.01 % EPR 3
% 16.71/8.01 % Horn 16
% 16.71/8.01 % unary 4
% 16.71/8.01 % binary 8
% 16.71/8.01 % lits 47
% 16.71/8.01 % lits eq 8
% 16.71/8.01 % fd_pure 0
% 16.71/8.01 % fd_pseudo 0
% 16.71/8.01 % fd_cond 0
% 16.71/8.01 % fd_pseudo_cond 5
% 16.71/8.01 % AC symbols 0
% 16.71/8.01
% 16.71/8.01 % ------ Input Options Time Limit: Unbounded
% 16.71/8.01
% 16.71/8.01
% 16.71/8.01 % ------
% 16.71/8.01 % Current options:
% 16.71/8.01 % ------
% 16.71/8.01
% 16.71/8.01
% 16.71/8.01 %
% 16.71/8.01
% 16.71/8.01 % ------ Proving...
% 16.71/8.01 %
% 16.71/8.01
% 16.71/8.01 % SZS status Theorem for theBenchmark.p
% 16.71/8.01
% 16.71/8.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 16.71/8.01
% 16.71/8.01
%------------------------------------------------------------------------------