%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET636+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 : n006.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 02:47:39 PM UTC 2026
% Result : Theorem 2.33s 1.23s
% Output : CNFRefutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 11
% Syntax : Number of formulae : 115 ( 18 unt; 1 def)
% Number of atoms : 335 ( 49 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 315 ( 126 ~; 141 |; 35 &)
% ( 10 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 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 : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 211 ( 0 sgn 200 !; 11 ?; 101 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f2,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ~ intersect(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f5,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f6,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f7,axiom,
! [X0,X1] :
( intersect(X0,X1)
=> intersect(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_intersect) ).
fof(f8,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f11,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f12,conjecture,
! [X0,X1] :
( disjoint(X0,X1)
<=> intersection(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th118) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] :
( disjoint(X0,X1)
<=> intersection(X0,X1) = empty_set ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| intersect(X1,X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f16,plain,
? [X0,X1] :
( disjoint(X0,X1)
<~> intersection(X0,X1) = empty_set ),
inference(ennf_transformation,[],[f13]) ).
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(nnf_transformation,[],[f1]) ).
fof(f18,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,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( ~ intersect(X0,X1)
| ? [X2] :
( member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) )
| intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f20,plain,
! [X0,X1] :
( ( ~ intersect(X0,X1)
| ? [X3] :
( member(X3,X1)
& member(X3,X0) ) )
& ( ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) )
| intersect(X0,X1) ) ),
inference(rectify,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ intersect(X0,X1)
| ( member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) )
| intersect(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ~ intersect(X0,X1) )
& ( intersect(X0,X1)
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f23,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f24,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f23]) ).
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,[],[f15]) ).
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(sK1(X0,X1),X0)
& ~ member(sK1(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f26]) ).
fof(f28,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,[],[f11]) ).
fof(f29,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,[],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X1) )
& ( ~ member(X3,X1)
| member(X3,X0) ) ) )
& ( ( ( member(sK2(X0,X1),X0)
| member(sK2(X0,X1),X1) )
& ( ~ member(sK2(X0,X1),X0)
| ~ member(sK2(X0,X1),X1) ) )
| X0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f29]) ).
fof(f31,plain,
? [X0,X1] :
( ( disjoint(X0,X1)
| intersection(X0,X1) = empty_set )
& ( ~ disjoint(X0,X1)
| intersection(X0,X1) != empty_set ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f32,plain,
( ( disjoint(sK3,sK4)
| empty_set = intersection(sK3,sK4) )
& ( ~ disjoint(sK3,sK4)
| empty_set != intersection(sK3,sK4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f31]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f36,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f37,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f39,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f40,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X0,X1] :
( intersect(X0,X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f44,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f46,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| intersect(X1,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f48,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f53,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| member(sK2(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f30]) ).
fof(f55,plain,
( disjoint(sK3,sK4)
| empty_set = intersection(sK3,sK4) ),
inference(cnf_transformation,[],[f32]) ).
fof(f56,plain,
( ~ disjoint(sK3,sK4)
| empty_set != intersection(sK3,sK4) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( intersect(X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_55,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f39]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| intersect(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ~ disjoint(X0,X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f45]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( intersect(X1,X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( member(sK2(X0,X1),X1)
| member(sK2(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_69,negated_conjecture,
( ~ disjoint(sK3,sK4)
| ( intersection(sK3,sK4) != empty_set ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_70,negated_conjecture,
( disjoint(sK3,sK4)
| ( intersection(sK3,sK4) = empty_set ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( ~ intersect(X0,X1)
| ~ disjoint(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_57]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( ~ disjoint(X0,X1)
| ~ intersect(X0,X1) ),
inference(renaming,[status(thm)],[c_83]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X0)
| disjoint(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_56,c_53]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_99]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X1)
| disjoint(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_56,c_54]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| member(sK0(X0,X1),X1) ),
inference(renaming,[status(thm)],[c_101]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] :
( intersect(X1,X0)
| disjoint(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_56,c_62]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| intersect(X0,X1) ),
inference(renaming,[status(thm)],[c_103]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_104,c_84]) ).
tcf(c_329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ disjoint(X1,X3)
| ~ member(X4,X2)
| ~ member(X4,X0)
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_84]) ).
tcf(c_330,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ disjoint(X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(unflattening,[status(thm)],[c_329]) ).
tcf(c_356,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_155]) ).
tcf(c_358,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X0)
| disjoint(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_100]) ).
tcf(c_359,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_358]) ).
tcf(c_360,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X1)
| disjoint(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_102]) ).
tcf(c_361,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| member(sK0(X0,X1),X1) ),
inference(renaming,[status(thm)],[c_360]) ).
tcf(c_562,definition,
iPr_def_10 = intersection(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_563,negated_conjecture,
( disjoint(sK3,sK4)
| ( iPr_def_10 = empty_set ) ),
inference(demodulation,[status(thm)],[c_70,c_562]) ).
tcf(c_564,negated_conjecture,
( ~ disjoint(sK3,sK4)
| ( iPr_def_10 != empty_set ) ),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_954,plain,
( disjoint(sK4,sK3)
| ( empty_set = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_563,c_356]) ).
tcf(c_973,plain,
! [X0: $i] : subset(empty_set,X0),
inference(superposition,[status(thm)],[c_64,c_55]) ).
tcf(c_979,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(intersection(X0,X1),X2)
| member(sK1(intersection(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_64,c_50]) ).
tcf(c_982,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_562,c_50]) ).
tcf(c_996,plain,
! [X0: $i] :
( member(X0,sK4)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_562,c_51]) ).
tcf(c_1089,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,sK4)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_562,c_49]) ).
tcf(c_1156,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ subset(X0,empty_set) ),
inference(superposition,[status(thm)],[c_973,c_58]) ).
tcf(c_1175,plain,
! [X0: $i] :
( member(sK2(X0,empty_set),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_68,c_55]) ).
tcf(c_1181,plain,
! [X0: $i] :
( member(sK2(empty_set,X0),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_68,c_55]) ).
tcf(c_1338,plain,
( member(sK2(empty_set,iPr_def_10),sK4)
| ( empty_set = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_1181,c_996]) ).
tcf(c_1339,plain,
( member(sK2(empty_set,iPr_def_10),sK3)
| ( empty_set = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_1181,c_982]) ).
tcf(c_1426,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(intersection(X1,X0),X2)
| member(sK1(intersection(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_61,c_979]) ).
tcf(c_1479,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(intersection(X0,X1),X2)
| member(sK1(intersection(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_64,c_50]) ).
tcf(c_1534,plain,
! [X0: $i] :
( member(X0,sK4)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_562,c_51]) ).
tcf(c_1686,plain,
! [X0: $i] :
( ( empty_set = iPr_def_10 )
| ~ disjoint(sK4,X0)
| ~ member(sK2(empty_set,iPr_def_10),X0) ),
inference(superposition,[status(thm)],[c_1338,c_330]) ).
tcf(c_1753,plain,
( ( empty_set = iPr_def_10 )
| ~ disjoint(sK4,sK3)
| ~ member(sK2(empty_set,iPr_def_10),sK3) ),
inference(instantiation,[status(thm)],[c_1686]) ).
tcf(c_2570,plain,
! [X0: $i] :
( member(sK2(X0,empty_set),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_68,c_55]) ).
tcf(c_2790,plain,
! [X0: $i,X1: $i] :
( subset(intersection(iPr_def_10,X0),X1)
| member(sK1(intersection(X0,iPr_def_10),X1),sK4) ),
inference(superposition,[status(thm)],[c_1426,c_996]) ).
tcf(c_3257,plain,
( member(sK2(iPr_def_10,empty_set),sK4)
| ( empty_set = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_2570,c_1534]) ).
tcf(c_3612,plain,
empty_set = iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_3257,c_954,c_1339,c_1753]) ).
tcf(c_3620,plain,
! [X0: $i] : ~ member(X0,iPr_def_10),
inference(demodulation,[status(thm)],[c_55,c_3612]) ).
tcf(c_3715,plain,
! [X0: $i,X1: $i] : subset(intersection(iPr_def_10,X0),X1),
inference(superposition,[status(thm)],[c_1479,c_3620]) ).
tcf(c_4512,plain,
! [X0: $i,X1: $i] : subset(intersection(iPr_def_10,X0),X1),
inference(global_subsumption_just,[status(thm)],[c_2790,c_3715]) ).
tcf(c_4522,plain,
! [X0: $i] : intersection(iPr_def_10,X0) = empty_set,
inference(superposition,[status(thm)],[c_4512,c_1156]) ).
tcf(c_4572,plain,
! [X0: $i,X1: $i] :
( member(X0,empty_set)
| ~ member(X0,iPr_def_10)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_4522,c_49]) ).
tcf(c_4613,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,iPr_def_10)
| ~ member(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4572,c_55]) ).
tcf(c_4624,plain,
! [X0: $i] : ~ member(X0,iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_4613,c_3620]) ).
tcf(c_4626,plain,
! [X0: $i] :
( ~ member(X0,sK4)
| ~ member(X0,sK3) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1089,c_4624]) ).
tcf(c_4657,plain,
empty_set = iPr_def_10,
inference(superposition,[status(thm)],[c_1175,c_4624]) ).
tcf(c_4692,plain,
( ~ disjoint(sK3,sK4)
| ( iPr_def_10 != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_564,c_4657]) ).
tcf(c_4694,plain,
~ disjoint(sK3,sK4),
inference(equality_resolution_simp,[status(thm)],[c_4692]) ).
tcf(c_4706,plain,
! [X0: $i] :
( disjoint(sK3,X0)
| ~ member(sK0(sK3,X0),sK4) ),
inference(superposition,[status(thm)],[c_359,c_4626]) ).
tcf(c_5003,plain,
disjoint(sK3,sK4),
inference(superposition,[status(thm)],[c_361,c_4706]) ).
tcf(c_5010,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5003,c_4694]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET636+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.40 % Computer : n006.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.41 % DateTime : Thu Sep 24 11:31:47 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.45 Running first-order theorem proving
% 0.15/0.45 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
% 0.15/0.46
% 0.15/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.46
% 0.20/0.46 % Detected problem language: tptp
% 0.20/0.47 % Proving...
% 2.33/1.23 % SZS status Started for theBenchmark.p
% 2.33/1.23 % SZS status Theorem for theBenchmark.p
% 2.33/1.23
% 2.33/1.23 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.33/1.23
% 2.33/1.23 % ------ iProver source info
% 2.33/1.23
% 2.33/1.23 % git: date: 2026-07-19 20:42:38 +0200
% 2.33/1.23 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.33/1.23 % git: non_committed_changes: false
% 2.33/1.23
% 2.33/1.23 % ------ Parsing...
% 2.33/1.23 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.33/1.23
% 2.33/1.23 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.33/1.23
% 2.33/1.23 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.33/1.23
% 2.33/1.23 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.33/1.23 % ------ Proving...
% 2.33/1.23 % ------ Problem Properties
% 2.33/1.23
% 2.33/1.23 %
% 2.33/1.23 % clauses 19
% 2.33/1.23 % conjectures 2
% 2.33/1.23 % EPR 8
% 2.33/1.23 % Horn 14
% 2.33/1.23 % unary 4
% 2.33/1.23 % binary 9
% 2.33/1.23 % lits 40
% 2.33/1.23 % lits eq 7
% 2.33/1.23 % fd_pure 0
% 2.33/1.23 % fd_pseudo 0
% 2.33/1.23 % fd_cond 0
% 2.33/1.23 % fd_pseudo_cond 3
% 2.33/1.23 % AC symbols 0
% 2.33/1.23
% 2.33/1.23 % ------ Schedule dynamic 5 is on
% 2.33/1.23
% 2.33/1.23 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.33/1.23
% 2.33/1.23
% 2.33/1.23 % ------
% 2.33/1.23 % Current options:
% 2.33/1.23 % ------
% 2.33/1.23
% 2.33/1.23
% 2.33/1.23 %
% 2.33/1.23
% 2.33/1.23 % ------ Proving...
% 2.33/1.23 %
% 2.33/1.23
% 2.33/1.23 % SZS status Theorem for theBenchmark.p
% 2.33/1.23
% 2.33/1.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.33/1.23
% 2.33/1.23
%------------------------------------------------------------------------------