%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET609+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 : n026.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 02:47:33 PM UTC 2026
% Result : Theorem 26.94s 6.11s
% Output : CNFRefutation 26.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 14
% Syntax : Number of formulae : 132 ( 31 unt; 5 def)
% Number of atoms : 557 ( 41 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 358 ( 143 ~; 172 |; 34 &)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% 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 : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 209 ( 0 sgn 202 !; 7 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(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] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
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,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f10,conjecture,
! [X0,X1,X2] : difference(X0,difference(X1,X2)) = union(difference(X0,X1),intersection(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th81) ).
fof(f11,negated_conjecture,
~ ! [X0,X1,X2] : difference(X0,difference(X1,X2)) = union(difference(X0,X1),intersection(X0,X2)),
inference(negated_conjecture,[status(cth)],[f10]) ).
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] : difference(X0,difference(X1,X2)) != union(difference(X0,X1),intersection(X0,X2)),
inference(ennf_transformation,[],[f11]) ).
fof(f14,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(f15,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,[],[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(f22,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(f23,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,[],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK0(X0,X1),X0)
& ~ member(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f23]) ).
fof(f25,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,[],[f9]) ).
fof(f26,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,[],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X1) )
& ( ~ member(X3,X1)
| member(X3,X0) ) ) )
& ( ( ( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1) )
& ( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1) ) )
| X0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f26]) ).
fof(f28,plain,
difference(sK2,difference(sK3,sK4)) != union(difference(sK2,sK3),intersection(sK2,sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f13]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f37,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f40,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f41,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f43,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f44,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f46,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f49,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f27]) ).
fof(f50,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f27]) ).
fof(f51,plain,
difference(sK2,difference(sK3,sK4)) != union(difference(sK2,sK3),intersection(sK2,sK4)),
inference(cnf_transformation,[],[f28]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f41]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_66,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f46]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_69,negated_conjecture,
union(difference(sK2,sK3),intersection(sK2,sK4)) != difference(sK2,difference(sK3,sK4)),
inference(cnf_transformation,[],[f51]) ).
tcf(c_230,plain,
union(intersection(sK2,sK4),difference(sK2,sK3)) != difference(sK2,difference(sK3,sK4)),
inference(demodulation,[status(thm)],[c_69,c_61]) ).
tcf(c_405,definition,
iPr_def_10 = intersection(sK2,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_406,definition,
iPr_def_11 = difference(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_407,definition,
iPr_def_12 = union(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_408,definition,
iPr_def_13 = difference(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_409,definition,
iPr_def_14 = difference(sK2,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_410,plain,
iPr_def_12 != iPr_def_14,
inference(demodulation,[status(thm)],[c_230,c_408,c_409,c_406,c_405,c_407]) ).
tcf(c_683,plain,
! [X0: $i] :
( member(X0,iPr_def_12)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_407,c_49]) ).
tcf(c_693,plain,
! [X0: $i] :
( member(X0,iPr_def_12)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_407,c_50]) ).
tcf(c_704,plain,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_405,c_53]) ).
tcf(c_754,plain,
! [X0: $i] :
( member(X0,sK4)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_405,c_54]) ).
tcf(c_764,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| member(sK0(iPr_def_10,X0),sK4) ),
inference(superposition,[status(thm)],[c_64,c_754]) ).
tcf(c_776,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(difference(X0,X1),X2)
| member(sK0(difference(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_64,c_56]) ).
tcf(c_777,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_408,c_56]) ).
tcf(c_778,plain,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_406,c_56]) ).
tcf(c_779,plain,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_409,c_56]) ).
tcf(c_804,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| member(sK0(iPr_def_11,X0),sK2) ),
inference(superposition,[status(thm)],[c_64,c_778]) ).
tcf(c_819,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| member(X0,iPr_def_10)
| ~ member(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_407,c_51]) ).
tcf(c_849,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_13)
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_408,c_57]) ).
tcf(c_850,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_11)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_406,c_57]) ).
tcf(c_851,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_14)
| ~ member(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_409,c_57]) ).
tcf(c_913,plain,
! [X0: $i] :
( member(X0,iPr_def_14)
| member(X0,iPr_def_13)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_409,c_55]) ).
tcf(c_914,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(X3,X2)
| member(X3,X1)
| ~ member(X3,X0)
| ~ subset(difference(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_55,c_65]) ).
tcf(c_917,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,difference(X1,X2))
| member(sK0(X0,difference(X1,X2)),X2)
| ~ member(sK0(X0,difference(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_55,c_63]) ).
tcf(c_983,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| ~ member(sK0(iPr_def_10,X0),iPr_def_13) ),
inference(superposition,[status(thm)],[c_764,c_849]) ).
tcf(c_1003,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| ~ member(sK0(iPr_def_11,X0),sK3) ),
inference(superposition,[status(thm)],[c_64,c_850]) ).
tcf(c_1022,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,sK4)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_405,c_52]) ).
tcf(c_1118,plain,
! [X0: $i] :
( member(sK1(iPr_def_14,X0),sK2)
| member(sK1(iPr_def_14,X0),X0)
| ( X0 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_68,c_779]) ).
tcf(c_2017,plain,
! [X0: $i,X1: $i] : subset(difference(X0,X1),X0),
inference(superposition,[status(thm)],[c_776,c_63]) ).
tcf(c_2178,plain,
! [X0: $i,X1: $i] :
( ( difference(X0,X1) = X0 )
| ~ subset(X0,difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_2017,c_58]) ).
tcf(c_12804,plain,
! [X0: $i,X1: $i] :
( member(X0,sK4)
| member(X0,X1)
| ~ subset(iPr_def_13,X1)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_408,c_914]) ).
tcf(c_12805,plain,
! [X0: $i,X1: $i] :
( member(X0,sK3)
| member(X0,X1)
| ~ subset(iPr_def_11,X1)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_406,c_914]) ).
tcf(c_14613,plain,
! [X0: $i,X1: $i] :
( subset(X0,difference(X0,X1))
| member(sK0(X0,difference(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_64,c_917]) ).
tcf(c_14663,plain,
! [X0: $i] :
( subset(X0,difference(sK2,iPr_def_13))
| member(sK0(X0,difference(sK2,iPr_def_13)),iPr_def_13)
| ~ member(sK0(X0,iPr_def_14),sK2) ),
inference(superposition,[status(thm)],[c_409,c_917]) ).
tcf(c_14755,plain,
! [X0: $i] :
( subset(X0,iPr_def_14)
| member(sK0(X0,iPr_def_14),iPr_def_13)
| ~ member(sK0(X0,iPr_def_14),sK2) ),
inference(light_normalisation,[status(thm)],[c_14663,c_409]) ).
tcf(c_20507,plain,
subset(iPr_def_10,difference(iPr_def_10,iPr_def_13)),
inference(superposition,[status(thm)],[c_14613,c_983]) ).
tcf(c_21027,plain,
difference(iPr_def_10,iPr_def_13) = iPr_def_10,
inference(superposition,[status(thm)],[c_20507,c_2178]) ).
tcf(c_21074,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_13)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_21027,c_57]) ).
tcf(c_51837,plain,
( member(sK1(iPr_def_14,iPr_def_12),iPr_def_11)
| member(sK1(iPr_def_14,iPr_def_12),iPr_def_10)
| member(sK1(iPr_def_14,iPr_def_12),sK2)
| ( iPr_def_12 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1118,c_819]) ).
tcf(c_51889,plain,
( member(sK1(iPr_def_14,iPr_def_12),iPr_def_11)
| member(sK1(iPr_def_14,iPr_def_12),iPr_def_10)
| member(sK1(iPr_def_14,iPr_def_12),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51837,c_410]) ).
tcf(c_52042,plain,
member(sK1(iPr_def_14,iPr_def_12),sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_51889,c_778,c_704]) ).
tcf(c_52044,plain,
( member(sK1(iPr_def_14,iPr_def_12),iPr_def_10)
| ~ member(sK1(iPr_def_14,iPr_def_12),sK4) ),
inference(superposition,[status(thm)],[c_52042,c_1022]) ).
tcf(c_52045,plain,
( member(sK1(iPr_def_14,iPr_def_12),iPr_def_14)
| member(sK1(iPr_def_14,iPr_def_12),iPr_def_13) ),
inference(superposition,[status(thm)],[c_52042,c_913]) ).
tcf(c_52160,plain,
( member(sK1(iPr_def_14,iPr_def_12),iPr_def_13)
| ( iPr_def_12 = iPr_def_14 )
| ~ member(sK1(iPr_def_14,iPr_def_12),iPr_def_12) ),
inference(superposition,[status(thm)],[c_52045,c_67]) ).
tcf(c_52165,plain,
( member(sK1(iPr_def_14,iPr_def_12),iPr_def_13)
| ~ member(sK1(iPr_def_14,iPr_def_12),iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_52160,c_410]) ).
tcf(c_61531,plain,
! [X0: $i] :
( member(sK1(iPr_def_14,iPr_def_12),sK3)
| member(sK1(iPr_def_14,iPr_def_12),X0)
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_52042,c_12805]) ).
tcf(c_63514,plain,
( subset(iPr_def_11,iPr_def_14)
| member(sK0(iPr_def_11,iPr_def_14),iPr_def_13) ),
inference(superposition,[status(thm)],[c_804,c_14755]) ).
tcf(c_63960,plain,
( subset(iPr_def_11,iPr_def_14)
| member(sK0(iPr_def_11,iPr_def_14),sK3) ),
inference(superposition,[status(thm)],[c_63514,c_777]) ).
tcf(c_64833,plain,
subset(iPr_def_11,iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_63960,c_1003]) ).
tcf(c_65001,plain,
( member(sK1(iPr_def_14,iPr_def_12),sK3)
| ( iPr_def_12 = iPr_def_14 )
| ~ subset(iPr_def_11,iPr_def_14)
| ~ member(sK1(iPr_def_14,iPr_def_12),iPr_def_12) ),
inference(superposition,[status(thm)],[c_61531,c_67]) ).
tcf(c_65011,plain,
( member(sK1(iPr_def_14,iPr_def_12),iPr_def_12)
| member(sK1(iPr_def_14,iPr_def_12),sK3)
| ~ subset(iPr_def_11,iPr_def_11) ),
inference(superposition,[status(thm)],[c_61531,c_693]) ).
tcf(c_65052,plain,
( member(sK1(iPr_def_14,iPr_def_12),iPr_def_12)
| member(sK1(iPr_def_14,iPr_def_12),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_65011,c_66]) ).
tcf(c_65093,plain,
( member(sK1(iPr_def_14,iPr_def_12),sK3)
| ~ member(sK1(iPr_def_14,iPr_def_12),iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_65001,c_410,c_64833]) ).
tcf(c_65096,plain,
member(sK1(iPr_def_14,iPr_def_12),sK3),
inference(backward_subsumption_resolution,[status(thm)],[c_65052,c_65093]) ).
tcf(c_65098,plain,
! [X0: $i] :
( member(sK1(iPr_def_14,iPr_def_12),sK4)
| member(sK1(iPr_def_14,iPr_def_12),X0)
| ~ subset(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_65096,c_12804]) ).
tcf(c_65504,plain,
! [X0: $i] :
( member(sK1(iPr_def_14,iPr_def_12),X0)
| ~ subset(iPr_def_13,X0)
| ~ member(sK1(iPr_def_14,iPr_def_12),iPr_def_13) ),
inference(superposition,[status(thm)],[c_65098,c_849]) ).
tcf(c_65505,plain,
! [X0: $i] :
( member(sK1(iPr_def_14,iPr_def_12),iPr_def_10)
| member(sK1(iPr_def_14,iPr_def_12),X0)
| ~ subset(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_65098,c_52044]) ).
tcf(c_85286,plain,
! [X0: $i] :
( member(sK1(iPr_def_14,iPr_def_12),iPr_def_12)
| member(sK1(iPr_def_14,iPr_def_12),X0)
| ~ subset(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_65505,c_683]) ).
tcf(c_92631,plain,
! [X0: $i] :
( member(sK1(iPr_def_14,iPr_def_12),X0)
| ~ subset(iPr_def_13,X0) ),
inference(global_subsumption_just,[status(thm)],[c_65504,c_52165,c_65504,c_85286]) ).
tcf(c_92661,plain,
( ~ subset(iPr_def_13,iPr_def_13)
| ~ member(sK1(iPr_def_14,iPr_def_12),iPr_def_14) ),
inference(superposition,[status(thm)],[c_92631,c_851]) ).
tcf(c_92673,plain,
~ member(sK1(iPr_def_14,iPr_def_12),iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_92661,c_66]) ).
tcf(c_92692,plain,
member(sK1(iPr_def_14,iPr_def_12),iPr_def_13),
inference(backward_subsumption_resolution,[status(thm)],[c_52045,c_92673]) ).
tcf(c_93020,plain,
( member(sK1(iPr_def_14,iPr_def_12),iPr_def_12)
| ( iPr_def_12 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_68,c_92673]) ).
tcf(c_93024,plain,
member(sK1(iPr_def_14,iPr_def_12),iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_93020,c_410]) ).
tcf(c_93026,plain,
( member(sK1(iPr_def_14,iPr_def_12),iPr_def_11)
| member(sK1(iPr_def_14,iPr_def_12),iPr_def_10) ),
inference(superposition,[status(thm)],[c_93024,c_819]) ).
tcf(c_93206,plain,
( member(sK1(iPr_def_14,iPr_def_12),iPr_def_10)
| ~ member(sK1(iPr_def_14,iPr_def_12),sK3) ),
inference(superposition,[status(thm)],[c_93026,c_850]) ).
tcf(c_93209,plain,
member(sK1(iPr_def_14,iPr_def_12),iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_93206,c_65096]) ).
tcf(c_93211,plain,
~ member(sK1(iPr_def_14,iPr_def_12),iPr_def_13),
inference(superposition,[status(thm)],[c_93209,c_21074]) ).
tcf(c_93216,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_93211,c_92692]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET609+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.58 % Computer : n026.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Thu Sep 24 11:29:11 UTC 2026
% 0.10/0.59 % CPUTime :
% 0.10/0.59 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.63 Running first-order theorem proving
% 0.10/0.63 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
% 0.14/0.64
% 0.14/0.64 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.64
% 0.14/0.64 % Detected problem language: tptp
% 0.14/0.65 % Proving...
% 26.94/6.11 % SZS status Started for theBenchmark.p
% 26.94/6.11 % SZS status Theorem for theBenchmark.p
% 26.94/6.11
% 26.94/6.11 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 26.94/6.11
% 26.94/6.11 % ------ iProver source info
% 26.94/6.11
% 26.94/6.11 % git: date: 2026-07-19 20:42:38 +0200
% 26.94/6.11 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 26.94/6.11 % git: non_committed_changes: false
% 26.94/6.11
% 26.94/6.11 % ------ Parsing...
% 26.94/6.11 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 26.94/6.11
% 26.94/6.11 % ------ 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 %
% 26.94/6.11
% 26.94/6.11 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 26.94/6.11
% 26.94/6.11 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 26.94/6.11 % ------ Proving...
% 26.94/6.11 % ------ Problem Properties
% 26.94/6.11
% 26.94/6.11 %
% 26.94/6.11 % clauses 24
% 26.94/6.11 % conjectures 0
% 26.94/6.11 % EPR 4
% 26.94/6.11 % Horn 20
% 26.94/6.11 % unary 9
% 26.94/6.11 % binary 8
% 26.94/6.11 % lits 46
% 26.94/6.11 % lits eq 11
% 26.94/6.11 % fd_pure 0
% 26.94/6.11 % fd_pseudo 0
% 26.94/6.11 % fd_cond 0
% 26.94/6.11 % fd_pseudo_cond 3
% 26.94/6.11 % AC symbols 0
% 26.94/6.11
% 26.94/6.11 % ------ Schedule dynamic 5 is on
% 26.94/6.11
% 26.94/6.11 % ------ no conjectures: strip conj schedule
% 26.94/6.11
% 26.94/6.11 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 26.94/6.11
% 26.94/6.11
% 26.94/6.11 % ------
% 26.94/6.11 % Current options:
% 26.94/6.11 % ------
% 26.94/6.11
% 26.94/6.11
% 26.94/6.11 %
% 26.94/6.11
% 26.94/6.11 % ------ Proving...
% 26.94/6.11 %
% 26.94/6.11
% 26.94/6.11 % SZS status Theorem for theBenchmark.p
% 26.94/6.11
% 26.94/6.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 26.94/6.12
% 26.94/6.12
%------------------------------------------------------------------------------