%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET105+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n017.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 02:46:37 PM UTC 2026
% Result : Theorem 4.70s 2.07s
% Output : CNFRefutation 4.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 20
% Syntax : Number of formulae : 156 ( 53 unt; 6 def)
% Number of atoms : 491 ( 99 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 329 ( 126 ~; 144 |; 49 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 194 ( 0 sgn 186 !; 8 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',subclass_defn) ).
fof(f2,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',class_elements_are_sets) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subclass(X1,X0)
& subclass(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',extensionality) ).
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
fof(f5,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',ordered_pair_defn) ).
fof(f13,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',intersection) ).
fof(f14,axiom,
! [X0,X1] :
( member(X1,complement(X0))
<=> ( ~ member(X1,X0)
& member(X1,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',complement) ).
fof(f16,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',null_class_defn) ).
fof(f29,axiom,
! [X0] :
( inductive(X0)
<=> ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',inductive_defn) ).
fof(f30,axiom,
? [X0] :
( ! [X1] :
( inductive(X1)
=> subclass(X0,X1) )
& inductive(X0)
& member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',infinity) ).
fof(f41,axiom,
! [X0] :
( X0 != null_class
=> ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',regularity) ).
fof(f44,conjecture,
! [X0,X1] :
( member(X1,universal_class)
| member(X0,universal_class)
| unordered_pair(null_class,singleton(null_class)) = ordered_pair(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_3_of_ordered_pair) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] :
( member(X1,universal_class)
| member(X0,universal_class)
| unordered_pair(null_class,singleton(null_class)) = ordered_pair(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f47,plain,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f51,plain,
? [X0] :
( ! [X1] :
( ~ inductive(X1)
| subclass(X0,X1) )
& inductive(X0)
& member(X0,universal_class) ),
inference(ennf_transformation,[],[f30]) ).
fof(f57,plain,
! [X0] :
( null_class = X0
| ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) ) ),
inference(ennf_transformation,[],[f41]) ).
fof(f60,plain,
? [X0,X1] :
( ~ member(X1,universal_class)
& ~ member(X0,universal_class)
& ordered_pair(X0,X1) != unordered_pair(null_class,singleton(null_class)) ),
inference(ennf_transformation,[],[f45]) ).
fof(f61,plain,
! [X0,X1] :
( ( ~ subclass(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subclass(X0,X1) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f62,plain,
! [X0,X1] :
( ( ~ subclass(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subclass(X0,X1) ) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ( ~ subclass(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK0(X0,X1),X0)
& ~ member(sK0(X0,X1),X1) )
| subclass(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f62]) ).
fof(f64,plain,
! [X0,X1] :
( ( X0 != X1
| ( subclass(X1,X0)
& subclass(X0,X1) ) )
& ( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f65,plain,
! [X0,X1] :
( ( X0 != X1
| ( subclass(X1,X0)
& subclass(X0,X1) ) )
& ( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( ~ member(X0,unordered_pair(X1,X2))
| ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) ) )
& ( ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( ~ member(X0,unordered_pair(X1,X2))
| ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) ) )
& ( ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f66]) ).
fof(f72,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,[],[f13]) ).
fof(f73,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,[],[f72]) ).
fof(f74,plain,
! [X0,X1] :
( ( ~ member(X1,complement(X0))
| ( ~ member(X1,X0)
& member(X1,universal_class) ) )
& ( member(X1,X0)
| ~ member(X1,universal_class)
| member(X1,complement(X0)) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f75,plain,
! [X0,X1] :
( ( ~ member(X1,complement(X0))
| ( ~ member(X1,X0)
& member(X1,universal_class) ) )
& ( member(X1,X0)
| ~ member(X1,universal_class)
| member(X1,complement(X0)) ) ),
inference(flattening,[],[f74]) ).
fof(f86,plain,
! [X0] :
( ( ~ inductive(X0)
| ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) ) )
& ( ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0)
| inductive(X0) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f87,plain,
! [X0] :
( ( ~ inductive(X0)
| ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) ) )
& ( ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0)
| inductive(X0) ) ),
inference(flattening,[],[f86]) ).
fof(f88,plain,
( ! [X1] :
( ~ inductive(X1)
| subclass(sK1,X1) )
& inductive(sK1)
& member(sK1,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f51]) ).
fof(f101,plain,
! [X0] :
( null_class = X0
| ( disjoint(sK4(X0),X0)
& member(sK4(X0),X0)
& member(sK4(X0),universal_class) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f57]) ).
fof(f103,plain,
( ~ member(sK7,universal_class)
& ~ member(sK6,universal_class)
& unordered_pair(null_class,singleton(null_class)) != ordered_pair(sK6,sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f60]) ).
fof(f104,plain,
! [X3,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f105,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subclass(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f106,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subclass(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f107,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f2]) ).
fof(f110,plain,
! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f65]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f67]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,universal_class) ),
inference(cnf_transformation,[],[f67]) ).
fof(f113,plain,
! [X2,X0,X1] :
( X0 != X2
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f114,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f115,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f5]) ).
fof(f116,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f117,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[],[f7]) ).
fof(f128,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f129,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f73]) ).
fof(f131,plain,
! [X0,X1] :
( ~ member(X1,complement(X0))
| ~ member(X1,X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f133,plain,
! [X0,X1] :
( member(X1,X0)
| ~ member(X1,universal_class)
| member(X1,complement(X0)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f135,plain,
! [X0] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f16]) ).
fof(f160,plain,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f163,plain,
inductive(sK1),
inference(cnf_transformation,[],[f88]) ).
fof(f186,plain,
! [X0] :
( null_class = X0
| member(sK4(X0),X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f187,plain,
! [X0] :
( null_class = X0
| member(sK4(X0),universal_class) ),
inference(cnf_transformation,[],[f101]) ).
fof(f191,plain,
~ member(sK7,universal_class),
inference(cnf_transformation,[],[f103]) ).
fof(f192,plain,
~ member(sK6,universal_class),
inference(cnf_transformation,[],[f103]) ).
fof(f193,plain,
unordered_pair(null_class,singleton(null_class)) != ordered_pair(sK6,sK7),
inference(cnf_transformation,[],[f103]) ).
fof(f194,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f117,f116,f116]) ).
fof(f231,plain,
unordered_pair(null_class,unordered_pair(null_class,null_class)) != unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7))),
inference(definition_unfolding,[],[f193,f116,f194]) ).
fof(f234,plain,
! [X2,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X1,X2)) ),
inference(equality_resolution,[],[f114]) ).
fof(f235,plain,
! [X2,X1] :
( ~ member(X2,universal_class)
| member(X2,unordered_pair(X1,X2)) ),
inference(equality_resolution,[],[f113]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_52,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f107]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f234]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,universal_class)
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f115]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f128]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f131]) ).
tcf(c_77,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f135]) ).
tcf(c_98,plain,
! [X0: $i] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_101,plain,
inductive(sK1),
inference(cnf_transformation,[],[f163]) ).
tcf(c_123,plain,
! [X0: $i] :
( member(sK4(X0),universal_class)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_124,plain,
! [X0: $i] :
( member(sK4(X0),X0)
| ( X0 = null_class ) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_128,negated_conjecture,
unordered_pair(unordered_pair(sK6,sK6),unordered_pair(sK6,unordered_pair(sK7,sK7))) != unordered_pair(null_class,unordered_pair(null_class,null_class)),
inference(cnf_transformation,[],[f231]) ).
tcf(c_129,negated_conjecture,
~ member(sK6,universal_class),
inference(cnf_transformation,[],[f192]) ).
tcf(c_130,negated_conjecture,
~ member(sK7,universal_class),
inference(cnf_transformation,[],[f191]) ).
tcf(c_891,plain,
! [X0: $i] :
( member(null_class,X0)
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_98,c_101]) ).
tcf(c_892,plain,
member(null_class,sK1),
inference(unflattening,[status(thm)],[c_891]) ).
tcf(c_1562,definition,
iPr_def_10 = unordered_pair(sK6,sK6),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1563,definition,
iPr_def_11 = unordered_pair(sK7,sK7),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_1564,definition,
iPr_def_12 = unordered_pair(sK6,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_1565,definition,
iPr_def_13 = unordered_pair(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_1566,definition,
iPr_def_14 = unordered_pair(null_class,null_class),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_1567,definition,
iPr_def_15 = unordered_pair(null_class,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_1568,negated_conjecture,
~ member(sK7,universal_class),
inference(demodulation,[status(thm)],[c_130]) ).
tcf(c_1569,negated_conjecture,
~ member(sK6,universal_class),
inference(demodulation,[status(thm)],[c_129]) ).
tcf(c_1570,negated_conjecture,
iPr_def_13 != iPr_def_15,
inference(demodulation,[status(thm)],[c_128,c_1566,c_1567,c_1563,c_1564,c_1562,c_1565]) ).
tcf(c_2405,plain,
member(iPr_def_11,universal_class),
inference(superposition,[status(thm)],[c_1563,c_60]) ).
tcf(c_2507,plain,
( member(null_class,iPr_def_14)
| ~ member(null_class,universal_class) ),
inference(superposition,[status(thm)],[c_1566,c_56]) ).
tcf(c_2529,plain,
( member(iPr_def_11,iPr_def_12)
| ~ member(iPr_def_11,universal_class) ),
inference(superposition,[status(thm)],[c_1564,c_57]) ).
tcf(c_2534,plain,
member(iPr_def_11,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_2529,c_2405]) ).
tcf(c_2545,plain,
! [X0: $i] :
( member(X0,universal_class)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_1563,c_58]) ).
tcf(c_2546,plain,
! [X0: $i] :
( member(X0,universal_class)
| ~ member(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_1564,c_58]) ).
tcf(c_2630,plain,
( member(sK4(iPr_def_11),universal_class)
| ( null_class = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_124,c_2545]) ).
tcf(c_2844,plain,
! [X0: $i] :
( member(null_class,X0)
| ~ subclass(sK1,X0) ),
inference(superposition,[status(thm)],[c_892,c_51]) ).
tcf(c_3079,plain,
member(null_class,universal_class),
inference(superposition,[status(thm)],[c_52,c_2844]) ).
tcf(c_3082,plain,
member(null_class,iPr_def_14),
inference(backward_subsumption_resolution,[status(thm)],[c_2507,c_3079]) ).
tcf(c_3547,plain,
! [X0: $i,X1: $i] :
( ( unordered_pair(X0,X1) = null_class )
| ( sK4(unordered_pair(X0,X1)) = X1 )
| ( sK4(unordered_pair(X0,X1)) = X0 ) ),
inference(superposition,[status(thm)],[c_124,c_59]) ).
tcf(c_3548,plain,
! [X0: $i] :
( ( X0 = null_class )
| ~ member(X0,iPr_def_14) ),
inference(superposition,[status(thm)],[c_1566,c_59]) ).
tcf(c_3549,plain,
! [X0: $i] :
( ( X0 = sK6 )
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1562,c_59]) ).
tcf(c_3989,plain,
( ( sK4(iPr_def_11) = sK7 )
| ( unordered_pair(sK7,sK7) = null_class )
| ( sK4(unordered_pair(sK7,sK7)) = sK7 ) ),
inference(superposition,[status(thm)],[c_1563,c_3547]) ).
tcf(c_4035,plain,
( ( null_class = iPr_def_11 )
| ( sK4(iPr_def_11) = sK7 ) ),
inference(light_normalisation,[status(thm)],[c_3989,c_1563]) ).
tcf(c_5665,plain,
( member(sK7,universal_class)
| ( null_class = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_4035,c_2630]) ).
tcf(c_5666,plain,
null_class = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_5665,c_1568]) ).
tcf(c_5671,plain,
! [X0: $i] :
( ( X0 = iPr_def_11 )
| ~ member(X0,iPr_def_14) ),
inference(demodulation,[status(thm)],[c_3548,c_5666]) ).
tcf(c_5686,plain,
member(iPr_def_11,iPr_def_14),
inference(demodulation,[status(thm)],[c_3082,c_5666]) ).
tcf(c_5696,plain,
! [X0: $i] :
( member(sK4(X0),X0)
| ( X0 = iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_124,c_5666]) ).
tcf(c_5697,plain,
! [X0: $i] :
( member(sK4(X0),universal_class)
| ( X0 = iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_123,c_5666]) ).
tcf(c_5700,plain,
unordered_pair(iPr_def_11,iPr_def_14) = iPr_def_15,
inference(demodulation,[status(thm)],[c_1567,c_5666]) ).
tcf(c_5702,plain,
! [X0: $i] : ~ member(X0,iPr_def_11),
inference(demodulation,[status(thm)],[c_77,c_5666]) ).
tcf(c_6216,plain,
! [X0: $i] :
( subclass(iPr_def_14,X0)
| ( sK0(iPr_def_14,X0) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_50,c_5671]) ).
tcf(c_6892,plain,
( ( iPr_def_10 = iPr_def_11 )
| ( sK4(iPr_def_10) = sK6 ) ),
inference(superposition,[status(thm)],[c_5696,c_3549]) ).
tcf(c_7619,plain,
( member(sK6,universal_class)
| ( iPr_def_10 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_6892,c_5697]) ).
tcf(c_7624,plain,
iPr_def_10 = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_7619,c_1569]) ).
tcf(c_7632,plain,
! [X0: $i] :
( subclass(iPr_def_14,X0)
| ( sK0(iPr_def_14,X0) = iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_6216,c_7624]) ).
tcf(c_7637,plain,
! [X0: $i] :
( member(sK4(X0),universal_class)
| ( X0 = iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_5697,c_7624]) ).
tcf(c_7638,plain,
! [X0: $i] :
( member(sK4(X0),X0)
| ( X0 = iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_5696,c_7624]) ).
tcf(c_7652,plain,
unordered_pair(iPr_def_10,iPr_def_14) = iPr_def_15,
inference(demodulation,[status(thm)],[c_5700,c_7624]) ).
tcf(c_7655,plain,
! [X0: $i] : ~ member(X0,iPr_def_10),
inference(demodulation,[status(thm)],[c_5702,c_7624]) ).
tcf(c_7662,plain,
member(iPr_def_10,iPr_def_14),
inference(demodulation,[status(thm)],[c_5686,c_7624]) ).
tcf(c_7677,plain,
member(iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_2534,c_7624]) ).
tcf(c_7678,plain,
unordered_pair(sK6,iPr_def_10) = iPr_def_12,
inference(demodulation,[status(thm)],[c_1564,c_7624]) ).
tcf(c_8287,plain,
! [X0: $i] :
( ( X0 = iPr_def_10 )
| ( X0 = sK6 )
| ~ member(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_7678,c_59]) ).
tcf(c_8727,plain,
! [X0: $i,X1: $i] :
( member(sK4(intersection(X0,X1)),X1)
| ( intersection(X0,X1) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_7638,c_73]) ).
tcf(c_8728,plain,
! [X0: $i,X1: $i] :
( member(sK4(intersection(X0,X1)),X0)
| ( intersection(X0,X1) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_7638,c_72]) ).
tcf(c_11657,plain,
! [X0: $i] :
( ( intersection(X0,iPr_def_12) = iPr_def_10 )
| ( sK4(intersection(X0,iPr_def_12)) = iPr_def_10 )
| ( sK4(intersection(X0,iPr_def_12)) = sK6 ) ),
inference(superposition,[status(thm)],[c_8727,c_8287]) ).
tcf(c_15567,plain,
! [X0: $i] :
( member(sK6,universal_class)
| ( intersection(X0,iPr_def_12) = iPr_def_10 )
| ( sK4(intersection(X0,iPr_def_12)) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_11657,c_7637]) ).
tcf(c_15580,plain,
! [X0: $i] :
( ( intersection(X0,iPr_def_12) = iPr_def_10 )
| ( sK4(intersection(X0,iPr_def_12)) = iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15567,c_1569]) ).
tcf(c_15867,plain,
! [X0: $i] :
( member(iPr_def_10,X0)
| ( intersection(X0,iPr_def_12) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_15580,c_8728]) ).
tcf(c_15893,plain,
! [X0: $i] :
( ( intersection(complement(X0),iPr_def_12) = iPr_def_10 )
| ~ member(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_15867,c_76]) ).
tcf(c_17020,plain,
intersection(complement(iPr_def_14),iPr_def_12) = iPr_def_10,
inference(superposition,[status(thm)],[c_7662,c_15893]) ).
tcf(c_17208,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,iPr_def_12)
| ~ member(X0,complement(iPr_def_14)) ),
inference(superposition,[status(thm)],[c_17020,c_71]) ).
tcf(c_17214,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_12)
| ~ member(X0,complement(iPr_def_14)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17208,c_7655]) ).
tcf(c_17736,plain,
! [X0: $i] :
( member(X0,iPr_def_14)
| ~ member(X0,iPr_def_12)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_74,c_17214]) ).
tcf(c_20699,plain,
! [X0: $i] :
( member(X0,iPr_def_14)
| ~ member(X0,iPr_def_12) ),
inference(global_subsumption_just,[status(thm)],[c_17736,c_2546,c_17736]) ).
tcf(c_20706,plain,
! [X0: $i] :
( subclass(iPr_def_12,X0)
| member(sK0(iPr_def_12,X0),iPr_def_14) ),
inference(superposition,[status(thm)],[c_50,c_20699]) ).
tcf(c_20776,plain,
subclass(iPr_def_12,iPr_def_14),
inference(superposition,[status(thm)],[c_20706,c_49]) ).
tcf(c_20793,plain,
( ( iPr_def_12 = iPr_def_14 )
| ~ subclass(iPr_def_14,iPr_def_12) ),
inference(superposition,[status(thm)],[c_20776,c_53]) ).
tcf(c_20823,plain,
( ( iPr_def_12 = iPr_def_14 )
| ( sK0(iPr_def_14,iPr_def_12) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_7632,c_20793]) ).
tcf(c_23385,plain,
( subclass(iPr_def_14,iPr_def_12)
| ( iPr_def_12 = iPr_def_14 )
| ~ member(iPr_def_10,iPr_def_12) ),
inference(superposition,[status(thm)],[c_20823,c_49]) ).
tcf(c_23388,plain,
( subclass(iPr_def_14,iPr_def_12)
| ( iPr_def_12 = iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23385,c_7677]) ).
tcf(c_23391,plain,
iPr_def_12 = iPr_def_14,
inference(global_subsumption_just,[status(thm)],[c_23388,c_20793,c_23388]) ).
tcf(c_23524,plain,
unordered_pair(iPr_def_10,iPr_def_12) = iPr_def_15,
inference(demodulation,[status(thm)],[c_7652,c_23391]) ).
tcf(c_23540,plain,
iPr_def_13 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_23524,c_1565]) ).
tcf(c_23541,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_23540,c_1570]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET105+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 09:45:31 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 4.70/2.07 % SZS status Started for theBenchmark.p
% 4.70/2.07 % SZS status Theorem for theBenchmark.p
% 4.70/2.07
% 4.70/2.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.70/2.07
% 4.70/2.07 % ------ iProver source info
% 4.70/2.07
% 4.70/2.07 % git: date: 2026-07-19 20:42:38 +0200
% 4.70/2.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.70/2.07 % git: non_committed_changes: false
% 4.70/2.07
% 4.70/2.07 % ------ Parsing...
% 4.70/2.07 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.70/2.07
% 4.70/2.07 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 4.70/2.07
% 4.70/2.07 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.70/2.07
% 4.70/2.07 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.70/2.07 % ------ Proving...
% 4.70/2.07 % ------ Problem Properties
% 4.70/2.07
% 4.70/2.07 %
% 4.70/2.07 % clauses 83
% 4.70/2.07 % conjectures 3
% 4.70/2.07 % EPR 10
% 4.70/2.07 % Horn 75
% 4.70/2.07 % unary 23
% 4.70/2.07 % binary 39
% 4.70/2.07 % lits 165
% 4.70/2.07 % lits eq 21
% 4.70/2.07 % fd_pure 0
% 4.70/2.07 % fd_pseudo 0
% 4.70/2.07 % fd_cond 4
% 4.70/2.07 % fd_pseudo_cond 3
% 4.70/2.07 % AC symbols 0
% 4.70/2.07
% 4.70/2.07 % ------ Schedule dynamic 5 is on
% 4.70/2.07
% 4.70/2.07 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.70/2.07
% 4.70/2.07
% 4.70/2.07 % ------
% 4.70/2.07 % Current options:
% 4.70/2.07 % ------
% 4.70/2.07
% 4.70/2.07
% 4.70/2.07 %
% 4.70/2.07
% 4.70/2.07 % ------ Proving...
% 4.70/2.07 %
% 4.70/2.07
% 4.70/2.07 % SZS status Theorem for theBenchmark.p
% 4.70/2.07
% 4.70/2.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.70/2.08
%------------------------------------------------------------------------------