%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET612+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 : n003.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 18.02s 3.62s
% Output : CNFRefutation 18.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 18
% Syntax : Number of formulae : 127 ( 38 unt; 5 def)
% Number of atoms : 502 ( 44 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 317 ( 132 ~; 145 |; 30 &)
% ( 7 <=>; 3 =>; 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 : 197 ( 0 sgn 190 !; 7 ?; 70 :)
% 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] : subset(X0,union(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_of_union) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_subsets) ).
fof(f6,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(difference(X2,X1),difference(X2,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_difference) ).
fof(f8,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f10,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f11,axiom,
! [X0] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(f12,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f13,conjecture,
! [X0,X1,X2] : difference(X0,union(X1,X2)) = intersection(difference(X0,X1),difference(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th85) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] : difference(X0,union(X1,X2)) = intersection(difference(X0,X1),difference(X0,X2)),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,intersection(X1,X2)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,intersection(X1,X2)) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(difference(X2,X1),difference(X2,X0)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f18,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f19,plain,
? [X0,X1,X2] : difference(X0,union(X1,X2)) != intersection(difference(X0,X1),difference(X0,X2)),
inference(ennf_transformation,[],[f14]) ).
fof(f20,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(f21,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,[],[f20]) ).
fof(f22,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(f23,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,[],[f22]) ).
fof(f24,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(f25,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,[],[f24]) ).
fof(f28,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,[],[f18]) ).
fof(f29,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,[],[f28]) ).
fof(f30,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))],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X2] :
( ( ~ member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X1)
| member(X2,X0) ) ) )
& ( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f32,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,[],[f31]) ).
fof(f33,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))],[f32]) ).
fof(f34,plain,
difference(sK2,union(sK3,sK4)) != intersection(difference(sK2,sK3),difference(sK2,sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f19]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f43,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f25]) ).
fof(f44,plain,
! [X0,X1] : subset(X0,union(X0,X1)),
inference(cnf_transformation,[],[f4]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ subset(X0,X2)
| ~ subset(X0,X1)
| subset(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(difference(X2,X1),difference(X2,X0)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f50,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f52,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f53,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f54,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f55,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f58,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f33]) ).
fof(f59,plain,
! [X0,X1] :
( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f33]) ).
fof(f60,plain,
difference(sK2,union(sK3,sK4)) != intersection(difference(sK2,sK3),difference(sK2,sK4)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : subset(X0,union(X0,X1)),
inference(cnf_transformation,[],[f44]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,intersection(X2,X1))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(difference(X2,X1),difference(X2,X0))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f50]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_69,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f55]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(sK1(X0,X1),X1)
| ~ member(sK1(X0,X1),X0) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_72,negated_conjecture,
intersection(difference(sK2,sK3),difference(sK2,sK4)) != difference(sK2,union(sK3,sK4)),
inference(cnf_transformation,[],[f60]) ).
tcf(c_456,definition,
iPr_def_10 = difference(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_457,definition,
iPr_def_11 = difference(sK2,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_458,definition,
iPr_def_12 = intersection(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_459,definition,
iPr_def_13 = union(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_460,definition,
iPr_def_14 = difference(sK2,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_461,negated_conjecture,
iPr_def_12 != iPr_def_14,
inference(demodulation,[status(thm)],[c_72,c_459,c_460,c_457,c_456,c_458]) ).
tcf(c_462,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_464,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_767,plain,
subset(sK3,iPr_def_13),
inference(superposition,[status(thm)],[c_459,c_58]) ).
tcf(c_768,plain,
! [X0: $i,X1: $i] : subset(X0,union(X1,X0)),
inference(superposition,[status(thm)],[c_64,c_58]) ).
tcf(c_784,plain,
subset(sK4,iPr_def_13),
inference(superposition,[status(thm)],[c_459,c_768]) ).
tcf(c_826,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_458,c_53]) ).
tcf(c_837,plain,
! [X0: $i] :
( subset(iPr_def_12,X0)
| member(sK0(iPr_def_12,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_67,c_826]) ).
tcf(c_891,plain,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_456,c_56]) ).
tcf(c_946,plain,
! [X0: $i] :
( subset(iPr_def_14,difference(sK2,X0))
| ~ subset(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_460,c_60]) ).
tcf(c_969,plain,
! [X0: $i] :
( ( iPr_def_12 = iPr_def_14 )
| ( iPr_def_14 != X0 )
| ( iPr_def_12 != X0 ) ),
inference(instantiation,[status(thm)],[c_464]) ).
tcf(c_976,plain,
! [X0: $i] :
( subset(iPr_def_12,X0)
| member(sK0(iPr_def_12,X0),sK2) ),
inference(superposition,[status(thm)],[c_837,c_891]) ).
tcf(c_1066,plain,
subset(iPr_def_12,sK2),
inference(superposition,[status(thm)],[c_976,c_66]) ).
tcf(c_1145,plain,
( ( iPr_def_12 = iPr_def_14 )
| ( iPr_def_14 != iPr_def_12 )
| ( iPr_def_12 != iPr_def_12 ) ),
inference(instantiation,[status(thm)],[c_969]) ).
tcf(c_1146,plain,
iPr_def_12 = iPr_def_12,
inference(instantiation,[status(thm)],[c_462]) ).
tcf(c_1219,plain,
( member(sK1(iPr_def_14,iPr_def_12),iPr_def_14)
| member(sK1(iPr_def_14,iPr_def_12),iPr_def_12)
| ( iPr_def_14 = iPr_def_12 ) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_1220,plain,
( ( iPr_def_14 = iPr_def_12 )
| ~ member(sK1(iPr_def_14,iPr_def_12),iPr_def_14)
| ~ member(sK1(iPr_def_14,iPr_def_12),iPr_def_12) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_1232,plain,
! [X0: $i] :
( subset(X0,iPr_def_12)
| ~ subset(X0,iPr_def_11)
| ~ subset(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_458,c_59]) ).
tcf(c_1859,plain,
( subset(iPr_def_14,iPr_def_10)
| ~ subset(sK3,iPr_def_13) ),
inference(superposition,[status(thm)],[c_456,c_946]) ).
tcf(c_1860,plain,
( subset(iPr_def_14,iPr_def_11)
| ~ subset(sK4,iPr_def_13) ),
inference(superposition,[status(thm)],[c_457,c_946]) ).
tcf(c_1863,plain,
subset(iPr_def_14,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_1860,c_784]) ).
tcf(c_1864,plain,
subset(iPr_def_14,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_1859,c_767]) ).
tcf(c_2470,plain,
( subset(iPr_def_14,iPr_def_12)
| ~ subset(iPr_def_14,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1863,c_1232]) ).
tcf(c_2471,plain,
subset(iPr_def_14,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_2470,c_1864]) ).
tcf(c_2492,plain,
! [X0: $i] :
( member(sK1(iPr_def_14,iPr_def_12),X0)
| ~ subset(iPr_def_12,X0)
| ~ member(sK1(iPr_def_14,iPr_def_12),iPr_def_12) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_2501,plain,
( member(sK1(iPr_def_14,iPr_def_12),sK2)
| ~ subset(iPr_def_12,sK2)
| ~ member(sK1(iPr_def_14,iPr_def_12),iPr_def_12) ),
inference(instantiation,[status(thm)],[c_2492]) ).
tcf(c_2748,plain,
! [X0: $i] :
( member(sK1(iPr_def_14,iPr_def_12),X0)
| ~ subset(iPr_def_14,X0)
| ~ member(sK1(iPr_def_14,iPr_def_12),iPr_def_14) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_10857,plain,
( member(sK1(iPr_def_14,iPr_def_12),iPr_def_12)
| ~ subset(iPr_def_14,iPr_def_12)
| ~ member(sK1(iPr_def_14,iPr_def_12),iPr_def_14) ),
inference(instantiation,[status(thm)],[c_2748]) ).
tcf(c_12914,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_458,c_53]) ).
tcf(c_12962,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| ~ member(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_458,c_54]) ).
tcf(c_12974,plain,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_460,c_56]) ).
tcf(c_13004,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_14)
| ~ member(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_460,c_57]) ).
tcf(c_13198,plain,
! [X0: $i] :
( member(X0,sK4)
| member(X0,sK3)
| ~ member(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_459,c_51]) ).
tcf(c_13213,plain,
! [X0: $i] :
( member(X0,iPr_def_14)
| member(X0,iPr_def_13)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_460,c_55]) ).
tcf(c_13699,plain,
! [X0: $i] :
( member(sK1(X0,iPr_def_12),iPr_def_11)
| member(sK1(X0,iPr_def_12),X0)
| ( X0 = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_71,c_12962]) ).
tcf(c_13700,plain,
! [X0: $i] :
( member(sK1(X0,iPr_def_12),iPr_def_10)
| member(sK1(X0,iPr_def_12),X0)
| ( X0 = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_71,c_12914]) ).
tcf(c_18097,plain,
( member(sK1(iPr_def_14,iPr_def_12),iPr_def_11)
| member(sK1(iPr_def_14,iPr_def_12),sK2)
| ( iPr_def_12 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_13699,c_12974]) ).
tcf(c_18102,plain,
( member(sK1(iPr_def_14,iPr_def_12),iPr_def_11)
| member(sK1(iPr_def_14,iPr_def_12),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18097,c_461]) ).
tcf(c_21197,plain,
member(sK1(iPr_def_14,iPr_def_12),sK2),
inference(global_subsumption_just,[status(thm)],[c_18102,c_461,c_1066,c_1145,c_1146,c_1220,c_1219,c_2471,c_2501,c_10857]) ).
tcf(c_21199,plain,
! [X0: $i] :
( member(sK1(iPr_def_14,iPr_def_12),X0)
| ~ subset(sK2,X0) ),
inference(superposition,[status(thm)],[c_21197,c_68]) ).
tcf(c_21213,plain,
( ~ subset(sK2,iPr_def_13)
| ~ member(sK1(iPr_def_14,iPr_def_12),iPr_def_14) ),
inference(superposition,[status(thm)],[c_21199,c_13004]) ).
tcf(c_22036,plain,
~ member(sK1(iPr_def_14,iPr_def_12),iPr_def_14),
inference(global_subsumption_just,[status(thm)],[c_21213,c_461,c_1145,c_1146,c_1220,c_2471,c_10857]) ).
tcf(c_22039,plain,
( member(sK1(iPr_def_14,iPr_def_12),iPr_def_10)
| ( iPr_def_12 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_13700,c_22036]) ).
tcf(c_22040,plain,
( member(sK1(iPr_def_14,iPr_def_12),iPr_def_11)
| ( iPr_def_12 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_13699,c_22036]) ).
tcf(c_22042,plain,
member(sK1(iPr_def_14,iPr_def_12),iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_22040,c_461]) ).
tcf(c_22043,plain,
member(sK1(iPr_def_14,iPr_def_12),iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_22039,c_461]) ).
tcf(c_22045,plain,
! [X0: $i] :
( member(sK1(iPr_def_14,iPr_def_12),X0)
| ~ subset(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_22042,c_68]) ).
tcf(c_22049,plain,
! [X0: $i] :
( member(sK1(iPr_def_14,iPr_def_12),X0)
| ~ subset(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_22043,c_68]) ).
tcf(c_25967,plain,
! [X0: $i,X1: $i] :
( ~ member(sK1(iPr_def_14,iPr_def_12),X1)
| ~ subset(iPr_def_11,difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_22045,c_57]) ).
tcf(c_26226,plain,
! [X0: $i,X1: $i] :
( ~ member(sK1(iPr_def_14,iPr_def_12),X1)
| ~ subset(iPr_def_10,difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_22049,c_57]) ).
tcf(c_40588,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_21197,c_13213]) ).
tcf(c_40591,plain,
member(sK1(iPr_def_14,iPr_def_12),iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_40588,c_22036]) ).
tcf(c_42502,plain,
( member(sK1(iPr_def_14,iPr_def_12),sK4)
| member(sK1(iPr_def_14,iPr_def_12),sK3) ),
inference(superposition,[status(thm)],[c_40591,c_13198]) ).
tcf(c_60279,plain,
( ~ subset(iPr_def_11,iPr_def_11)
| ~ member(sK1(iPr_def_14,iPr_def_12),sK4) ),
inference(superposition,[status(thm)],[c_457,c_25967]) ).
tcf(c_60281,plain,
~ member(sK1(iPr_def_14,iPr_def_12),sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_60279,c_69]) ).
tcf(c_60560,plain,
( ~ subset(iPr_def_10,iPr_def_10)
| ~ member(sK1(iPr_def_14,iPr_def_12),sK3) ),
inference(superposition,[status(thm)],[c_456,c_26226]) ).
tcf(c_60563,plain,
~ member(sK1(iPr_def_14,iPr_def_12),sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_60560,c_69]) ).
tcf(c_60566,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_60563,c_60281,c_42502]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET612+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 11:28:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 18.02/3.62 % SZS status Started for theBenchmark.p
% 18.02/3.62 % SZS status Theorem for theBenchmark.p
% 18.02/3.62
% 18.02/3.62 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 18.02/3.62
% 18.02/3.62 % ------ iProver source info
% 18.02/3.62
% 18.02/3.62 % git: date: 2026-07-19 20:42:38 +0200
% 18.02/3.62 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 18.02/3.62 % git: non_committed_changes: false
% 18.02/3.62
% 18.02/3.62 % ------ Parsing...
% 18.02/3.62 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 18.02/3.62
% 18.02/3.62 % ------ 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 %
% 18.02/3.62
% 18.02/3.62 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 18.02/3.62
% 18.02/3.62 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 18.02/3.62 % ------ Proving...
% 18.02/3.62 % ------ Problem Properties
% 18.02/3.62
% 18.02/3.62 %
% 18.02/3.62 % clauses 27
% 18.02/3.62 % conjectures 1
% 18.02/3.62 % EPR 4
% 18.02/3.62 % Horn 23
% 18.02/3.62 % unary 10
% 18.02/3.62 % binary 9
% 18.02/3.62 % lits 52
% 18.02/3.62 % lits eq 11
% 18.02/3.62 % fd_pure 0
% 18.02/3.62 % fd_pseudo 0
% 18.02/3.62 % fd_cond 0
% 18.02/3.62 % fd_pseudo_cond 3
% 18.02/3.62 % AC symbols 0
% 18.02/3.62
% 18.02/3.62 % ------ Schedule dynamic 5 is on
% 18.02/3.62
% 18.02/3.62 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 18.02/3.62
% 18.02/3.62
% 18.02/3.62 % ------
% 18.02/3.62 % Current options:
% 18.02/3.62 % ------
% 18.02/3.62
% 18.02/3.62
% 18.02/3.62 %
% 18.02/3.62
% 18.02/3.62 % ------ Proving...
% 18.02/3.62 %
% 18.02/3.62
% 18.02/3.62 % SZS status Theorem for theBenchmark.p
% 18.02/3.62
% 18.02/3.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.02/3.62
% 18.02/3.62
%------------------------------------------------------------------------------