%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET634+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 : n016.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 02:47:38 PM UTC 2026
% Result : Theorem 4.05s 2.47s
% Output : CNFRefutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of formulae : 129 ( 31 unt; 4 def)
% Number of atoms : 479 ( 49 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 311 ( 128 ~; 151 |; 23 &)
% ( 6 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 202 ( 0 sgn 195 !; 7 ?; 104 :)
% 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,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f5,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f8,axiom,
! [X0] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(f9,conjecture,
! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_difference_and_intersection) ).
fof(f10,negated_conjecture,
~ ! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),X2),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ? [X2] :
( member(X2,X0)
<~> member(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f1]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f13,plain,
? [X0,X1,X2] : intersection(X0,difference(X1,X2)) != difference(intersection(X0,X1),X2),
inference(ennf_transformation,[],[f10]) ).
fof(f14,plain,
! [X0,X1] :
( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f11]) ).
fof(f15,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))],[f14]) ).
fof(f16,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(f17,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,[],[f16]) ).
fof(f18,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(f19,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,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f21,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f20]) ).
fof(f25,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f26,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK2(X0,X1),X0)
& ~ member(sK2(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f26]) ).
fof(f28,plain,
intersection(sK3,difference(sK4,sK5)) != difference(intersection(sK3,sK4),sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f13]) ).
fof(f29,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| member(sK0(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X0)
| ~ member(sK0(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f36,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f39,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f40,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f45,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f46,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f48,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f49,plain,
intersection(sK3,difference(sK4,sK5)) != difference(intersection(sK3,sK4),sK5),
inference(cnf_transformation,[],[f28]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(sK0(X0,X1),X1)
| ~ member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X1)
| member(sK0(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f40]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_66,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f48]) ).
tcf(c_67,negated_conjecture,
intersection(sK3,difference(sK4,sK5)) != difference(intersection(sK3,sK4),sK5),
inference(cnf_transformation,[],[f49]) ).
tcf(c_387,definition,
iPr_def_10 = difference(sK4,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_388,definition,
iPr_def_11 = intersection(sK3,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_389,definition,
iPr_def_12 = intersection(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_390,definition,
iPr_def_13 = difference(iPr_def_12,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_391,negated_conjecture,
iPr_def_11 != iPr_def_13,
inference(demodulation,[status(thm)],[c_67,c_389,c_390,c_387,c_388]) ).
tcf(c_392,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_394,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_631,plain,
intersection(iPr_def_10,sK3) = iPr_def_11,
inference(demodulation,[status(thm)],[c_388,c_60]) ).
tcf(c_642,plain,
! [X0: $i] :
( member(X0,iPr_def_12)
| ~ member(X0,sK4)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_389,c_51]) ).
tcf(c_643,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| ~ member(X0,iPr_def_10)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_631,c_51]) ).
tcf(c_660,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(intersection(X0,X1),X2)
| member(sK2(intersection(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_64,c_52]) ).
tcf(c_663,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_389,c_52]) ).
tcf(c_664,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_631,c_52]) ).
tcf(c_682,plain,
! [X0: $i] :
( member(X0,sK4)
| ~ member(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_389,c_53]) ).
tcf(c_683,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_631,c_53]) ).
tcf(c_696,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(difference(X0,X1),X2)
| member(sK2(difference(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_64,c_55]) ).
tcf(c_697,plain,
! [X0: $i] :
( member(X0,sK4)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_387,c_55]) ).
tcf(c_698,plain,
! [X0: $i] :
( member(X0,iPr_def_12)
| ~ member(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_390,c_55]) ).
tcf(c_730,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| member(sK2(iPr_def_11,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_64,c_664]) ).
tcf(c_762,plain,
! [X0: $i] :
( subset(iPr_def_13,X0)
| member(sK2(iPr_def_13,X0),iPr_def_12) ),
inference(superposition,[status(thm)],[c_64,c_698]) ).
tcf(c_776,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| member(sK2(iPr_def_11,X0),sK4) ),
inference(superposition,[status(thm)],[c_730,c_697]) ).
tcf(c_791,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| member(X0,sK5)
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_387,c_54]) ).
tcf(c_792,plain,
! [X0: $i] :
( member(X0,iPr_def_13)
| member(X0,sK5)
| ~ member(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_390,c_54]) ).
tcf(c_794,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,difference(X1,X2))
| member(sK2(X0,difference(X1,X2)),X2)
| ~ member(sK2(X0,difference(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_54,c_63]) ).
tcf(c_807,plain,
! [X0: $i] :
( ( iPr_def_11 = iPr_def_13 )
| ( iPr_def_13 != X0 )
| ( iPr_def_11 != X0 ) ),
inference(instantiation,[status(thm)],[c_394]) ).
tcf(c_815,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_10)
| ~ member(X0,sK5) ),
inference(superposition,[status(thm)],[c_387,c_56]) ).
tcf(c_816,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_13)
| ~ member(X0,sK5) ),
inference(superposition,[status(thm)],[c_390,c_56]) ).
tcf(c_834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,X2)
| ~ member(X3,X1)
| ~ member(X3,X0)
| ~ subset(intersection(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_51,c_65]) ).
tcf(c_836,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,X2)
| member(sK2(X0,X2),X1)
| ~ subset(X0,X1) ),
inference(superposition,[status(thm)],[c_64,c_65]) ).
tcf(c_903,plain,
! [X0: $i] :
( member(sK0(X0,iPr_def_11),sK3)
| member(sK0(X0,iPr_def_11),X0)
| ( X0 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_50,c_683]) ).
tcf(c_1022,plain,
( ( iPr_def_11 = iPr_def_13 )
| ( iPr_def_13 != iPr_def_11 )
| ( iPr_def_11 != iPr_def_11 ) ),
inference(instantiation,[status(thm)],[c_807]) ).
tcf(c_1023,plain,
iPr_def_11 = iPr_def_11,
inference(instantiation,[status(thm)],[c_392]) ).
tcf(c_1068,plain,
! [X0: $i] :
( subset(iPr_def_13,X0)
| member(sK2(iPr_def_13,X0),sK4) ),
inference(superposition,[status(thm)],[c_762,c_682]) ).
tcf(c_1107,plain,
! [X0: $i,X1: $i] :
( subset(iPr_def_11,X1)
| member(sK2(iPr_def_11,X1),X0)
| ~ subset(sK4,X0) ),
inference(superposition,[status(thm)],[c_776,c_65]) ).
tcf(c_1124,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| ~ member(sK2(iPr_def_11,X0),sK5) ),
inference(superposition,[status(thm)],[c_730,c_815]) ).
tcf(c_1140,plain,
( member(sK0(iPr_def_13,iPr_def_11),iPr_def_13)
| member(sK0(iPr_def_13,iPr_def_11),iPr_def_11)
| ( iPr_def_13 = iPr_def_11 ) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_1141,plain,
( ( iPr_def_13 = iPr_def_11 )
| ~ member(sK0(iPr_def_13,iPr_def_11),iPr_def_13)
| ~ member(sK0(iPr_def_13,iPr_def_11),iPr_def_11) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_1166,plain,
! [X0: $i] :
( member(sK0(iPr_def_13,X0),X0)
| ( X0 = iPr_def_13 )
| ~ member(sK0(iPr_def_13,X0),sK5) ),
inference(superposition,[status(thm)],[c_50,c_816]) ).
tcf(c_1441,plain,
! [X0: $i,X1: $i] :
( subset(iPr_def_13,X1)
| member(sK2(iPr_def_13,X1),X0)
| ~ subset(sK4,X0) ),
inference(superposition,[status(thm)],[c_1068,c_65]) ).
tcf(c_1822,plain,
! [X0: $i,X1: $i] :
( subset(intersection(iPr_def_13,X0),X1)
| member(sK2(intersection(iPr_def_13,X0),X1),iPr_def_12) ),
inference(superposition,[status(thm)],[c_660,c_698]) ).
tcf(c_2188,plain,
! [X0: $i,X1: $i] : subset(difference(X0,X1),X0),
inference(superposition,[status(thm)],[c_696,c_63]) ).
tcf(c_2289,plain,
! [X0: $i,X1: $i] :
( ( difference(X0,X1) = X0 )
| ~ subset(X0,difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_2188,c_57]) ).
tcf(c_2307,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK2(X0,X1),sK3)
| ~ subset(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_836,c_663]) ).
tcf(c_2698,plain,
! [X0: $i,X1: $i] :
( member(sK0(iPr_def_13,X0),X1)
| ~ subset(X0,X1)
| ~ member(sK0(iPr_def_13,X0),X0) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_3296,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| ~ subset(sK4,X0) ),
inference(superposition,[status(thm)],[c_1107,c_63]) ).
tcf(c_3431,plain,
! [X0: $i,X1: $i] :
( subset(X0,difference(X0,X1))
| member(sK2(X0,difference(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_64,c_794]) ).
tcf(c_3628,plain,
! [X0: $i] :
( subset(iPr_def_13,X0)
| ~ subset(sK4,X0) ),
inference(superposition,[status(thm)],[c_1441,c_63]) ).
tcf(c_4608,plain,
! [X0: $i] : subset(intersection(iPr_def_13,X0),iPr_def_12),
inference(superposition,[status(thm)],[c_1822,c_63]) ).
tcf(c_5018,plain,
subset(iPr_def_11,difference(iPr_def_11,sK5)),
inference(superposition,[status(thm)],[c_3431,c_1124]) ).
tcf(c_5222,plain,
difference(iPr_def_11,sK5) = iPr_def_11,
inference(superposition,[status(thm)],[c_5018,c_2289]) ).
tcf(c_5251,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_11)
| ~ member(X0,sK5) ),
inference(superposition,[status(thm)],[c_5222,c_56]) ).
tcf(c_6810,plain,
! [X0: $i] :
( member(sK0(iPr_def_13,iPr_def_11),X0)
| ~ subset(iPr_def_11,X0)
| ~ member(sK0(iPr_def_13,iPr_def_11),iPr_def_11) ),
inference(instantiation,[status(thm)],[c_2698]) ).
tcf(c_7071,plain,
! [X0: $i] :
( subset(X0,sK3)
| ~ subset(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_2307,c_63]) ).
tcf(c_7141,plain,
! [X0: $i] : subset(intersection(iPr_def_13,X0),sK3),
inference(superposition,[status(thm)],[c_4608,c_7071]) ).
tcf(c_7150,plain,
! [X0: $i,X1: $i] :
( member(X0,sK3)
| ~ member(X0,iPr_def_13)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_7141,c_834]) ).
tcf(c_7245,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,iPr_def_13) ),
inference(global_subsumption_just,[status(thm)],[c_7150,c_663,c_698]) ).
tcf(c_7997,plain,
( member(sK0(iPr_def_13,iPr_def_11),sK3)
| ( iPr_def_11 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_903,c_7245]) ).
tcf(c_8005,plain,
member(sK0(iPr_def_13,iPr_def_11),sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_7997,c_391]) ).
tcf(c_8273,plain,
! [X0: $i] :
( member(sK0(iPr_def_13,iPr_def_11),X0)
| ~ subset(iPr_def_13,X0)
| ~ member(sK0(iPr_def_13,iPr_def_11),iPr_def_13) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_8461,plain,
! [X0: $i] :
( member(sK0(iPr_def_13,iPr_def_11),X0)
| ~ subset(sK3,X0) ),
inference(superposition,[status(thm)],[c_8005,c_65]) ).
tcf(c_8462,plain,
( member(sK0(iPr_def_13,iPr_def_11),iPr_def_11)
| ~ member(sK0(iPr_def_13,iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_8005,c_643]) ).
tcf(c_8463,plain,
( member(sK0(iPr_def_13,iPr_def_11),iPr_def_12)
| ~ member(sK0(iPr_def_13,iPr_def_11),sK4) ),
inference(superposition,[status(thm)],[c_8005,c_642]) ).
tcf(c_8522,plain,
( member(sK0(iPr_def_13,iPr_def_11),sK4)
| ~ subset(sK3,iPr_def_12) ),
inference(superposition,[status(thm)],[c_8461,c_682]) ).
tcf(c_8724,plain,
! [X0: $i] :
( member(sK0(iPr_def_13,iPr_def_11),X0)
| ~ subset(sK3,iPr_def_12)
| ~ subset(sK4,X0) ),
inference(superposition,[status(thm)],[c_8522,c_65]) ).
tcf(c_11771,plain,
! [X0: $i] :
( member(sK0(iPr_def_13,iPr_def_11),X0)
| ~ subset(sK4,X0) ),
inference(global_subsumption_just,[status(thm)],[c_8724,c_391,c_1022,c_1023,c_1140,c_3296,c_3628,c_6810,c_8273]) ).
tcf(c_11788,plain,
( member(sK0(iPr_def_13,iPr_def_11),iPr_def_10)
| member(sK0(iPr_def_13,iPr_def_11),sK5)
| ~ subset(sK4,sK4) ),
inference(superposition,[status(thm)],[c_11771,c_791]) ).
tcf(c_11799,plain,
( member(sK0(iPr_def_13,iPr_def_11),iPr_def_12)
| ~ subset(sK4,sK4) ),
inference(superposition,[status(thm)],[c_11771,c_8463]) ).
tcf(c_11803,plain,
member(sK0(iPr_def_13,iPr_def_11),iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_11799,c_66]) ).
tcf(c_11831,plain,
( member(sK0(iPr_def_13,iPr_def_11),iPr_def_10)
| member(sK0(iPr_def_13,iPr_def_11),sK5) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11788,c_66]) ).
tcf(c_12020,plain,
( member(sK0(iPr_def_13,iPr_def_11),iPr_def_13)
| member(sK0(iPr_def_13,iPr_def_11),sK5) ),
inference(superposition,[status(thm)],[c_11803,c_792]) ).
tcf(c_14291,plain,
member(sK0(iPr_def_13,iPr_def_11),sK5),
inference(global_subsumption_just,[status(thm)],[c_11831,c_391,c_1022,c_1023,c_1141,c_8462,c_11831,c_12020]) ).
tcf(c_14294,plain,
( member(sK0(iPr_def_13,iPr_def_11),iPr_def_11)
| ( iPr_def_11 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_14291,c_1166]) ).
tcf(c_14295,plain,
member(sK0(iPr_def_13,iPr_def_11),iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_14294,c_391]) ).
tcf(c_14301,plain,
~ member(sK0(iPr_def_13,iPr_def_11),sK5),
inference(superposition,[status(thm)],[c_14295,c_5251]) ).
tcf(c_14304,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_14301,c_14291]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET634+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.43 % Computer : n016.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Thu Sep 24 11:35:46 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.50 Running first-order theorem proving
% 0.16/0.50 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
% 0.25/0.52
% 0.25/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.25/0.52
% 0.25/0.52 % Detected problem language: tptp
% 0.25/0.53 % Proving...
% 4.05/2.47 % SZS status Started for theBenchmark.p
% 4.05/2.47 % SZS status Theorem for theBenchmark.p
% 4.05/2.47
% 4.05/2.47 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.05/2.47
% 4.05/2.47 % ------ iProver source info
% 4.05/2.47
% 4.05/2.47 % git: date: 2026-07-19 20:42:38 +0200
% 4.05/2.47 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.05/2.47 % git: non_committed_changes: false
% 4.05/2.47
% 4.05/2.47 % ------ Parsing...
% 4.05/2.47 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.05/2.47
% 4.05/2.47 % ------ 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 %
% 4.05/2.47
% 4.05/2.47 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.05/2.47
% 4.05/2.47 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.05/2.47 % ------ Proving...
% 4.05/2.47 % ------ Problem Properties
% 4.05/2.47
% 4.05/2.47 %
% 4.05/2.47 % clauses 21
% 4.05/2.47 % conjectures 1
% 4.05/2.47 % EPR 4
% 4.05/2.47 % Horn 17
% 4.05/2.47 % unary 7
% 4.05/2.47 % binary 6
% 4.05/2.47 % lits 43
% 4.05/2.47 % lits eq 11
% 4.05/2.47 % fd_pure 0
% 4.05/2.47 % fd_pseudo 0
% 4.05/2.47 % fd_cond 0
% 4.05/2.47 % fd_pseudo_cond 5
% 4.05/2.47 % AC symbols 0
% 4.05/2.47
% 4.05/2.47 % ------ Schedule dynamic 5 is on
% 4.05/2.47
% 4.05/2.47 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.05/2.47
% 4.05/2.47
% 4.05/2.47 % ------
% 4.05/2.47 % Current options:
% 4.05/2.47 % ------
% 4.05/2.47
% 4.05/2.47
% 4.05/2.47 %
% 4.05/2.47
% 4.05/2.47 % ------ Proving...
% 4.05/2.47 %
% 4.05/2.47
% 4.05/2.47 % SZS status Theorem for theBenchmark.p
% 4.05/2.47
% 4.05/2.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.05/2.47
% 4.05/2.47
%------------------------------------------------------------------------------