%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET096+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n013.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 02:46:34 PM UTC 2026
% Result : Theorem 65.45s 9.94s
% Output : CNFRefutation 65.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 20 unt; 0 def)
% Number of atoms : 142 ( 50 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 144 ( 57 ~; 56 |; 24 &)
% ( 4 <=>; 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 76 !; 6 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',subclass_defn) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subclass(X1,X0)
& subclass(X0,X1) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(f16,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',null_class_defn) ).
fof(f44,conjecture,
! [X0,X1] :
( subclass(X0,singleton(X1))
=> ( singleton(X1) = X0
| X0 = null_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_subsets_of_singleton) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] :
( subclass(X0,singleton(X1))
=> ( singleton(X1) = X0
| X0 = null_class ) ),
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(f60,plain,
? [X0,X1] :
( subclass(X0,singleton(X1))
& singleton(X1) != X0
& null_class != X0 ),
inference(ennf_transformation,[],[f45]) ).
fof(f61,plain,
? [X0,X1] :
( subclass(X0,singleton(X1))
& singleton(X1) != X0
& null_class != X0 ),
inference(flattening,[],[f60]) ).
fof(f62,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(f63,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,[],[f62]) ).
fof(f64,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))],[f63]) ).
fof(f65,plain,
! [X0,X1] :
( ( X0 != X1
| ( subclass(X1,X0)
& subclass(X0,X1) ) )
& ( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f66,plain,
! [X0,X1] :
( ( X0 != X1
| ( subclass(X1,X0)
& subclass(X0,X1) ) )
& ( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f65]) ).
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(nnf_transformation,[],[f4]) ).
fof(f68,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,[],[f67]) ).
fof(f104,plain,
( subclass(sK6,singleton(sK7))
& sK6 != singleton(sK7)
& null_class != sK6 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f61]) ).
fof(f105,plain,
! [X3,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f106,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subclass(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f107,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subclass(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f111,plain,
! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f66]) ).
fof(f112,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f68]) ).
fof(f117,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f136,plain,
! [X0] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f16]) ).
fof(f192,plain,
subclass(sK6,singleton(sK7)),
inference(cnf_transformation,[],[f104]) ).
fof(f193,plain,
sK6 != singleton(sK7),
inference(cnf_transformation,[],[f104]) ).
fof(f194,plain,
null_class != sK6,
inference(cnf_transformation,[],[f104]) ).
fof(f232,plain,
sK6 != unordered_pair(sK7,sK7),
inference(definition_unfolding,[],[f193,f117]) ).
fof(f233,plain,
subclass(sK6,unordered_pair(sK7,sK7)),
inference(definition_unfolding,[],[f192,f117]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( X0 = X1 )
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_77,plain,
! [X0: $i] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f136]) ).
tcf(c_128,negated_conjecture,
null_class != sK6,
inference(cnf_transformation,[],[f194]) ).
tcf(c_129,negated_conjecture,
unordered_pair(sK7,sK7) != sK6,
inference(cnf_transformation,[],[f232]) ).
tcf(c_130,negated_conjecture,
subclass(sK6,unordered_pair(sK7,sK7)),
inference(cnf_transformation,[],[f233]) ).
tcf(c_1813,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(unordered_pair(X0,X1),X2)
| ( sK0(unordered_pair(X0,X1),X2) = X1 )
| ( sK0(unordered_pair(X0,X1),X2) = X0 ) ),
inference(superposition,[status(thm)],[c_50,c_59]) ).
tcf(c_1894,plain,
( ( unordered_pair(sK7,sK7) = sK6 )
| ~ subclass(unordered_pair(sK7,sK7),sK6) ),
inference(superposition,[status(thm)],[c_130,c_53]) ).
tcf(c_1895,plain,
~ subclass(unordered_pair(sK7,sK7),sK6),
inference(global_subsumption_just,[status(thm)],[c_1894,c_129,c_1894]) ).
tcf(c_2261,plain,
sK0(unordered_pair(sK7,sK7),sK6) = sK7,
inference(superposition,[status(thm)],[c_1813,c_1895]) ).
tcf(c_3523,plain,
( subclass(unordered_pair(sK7,sK7),sK6)
| ~ member(sK7,sK6) ),
inference(superposition,[status(thm)],[c_2261,c_49]) ).
tcf(c_4591,plain,
! [X0: $i,X1: $i,X2: $i] :
( subclass(X0,X2)
| member(sK0(X0,X2),X1)
| ~ subclass(X0,X1) ),
inference(superposition,[status(thm)],[c_50,c_51]) ).
tcf(c_4632,plain,
! [X0: $i] : subclass(null_class,X0),
inference(superposition,[status(thm)],[c_50,c_77]) ).
tcf(c_4633,plain,
! [X0: $i] :
( ( X0 = null_class )
| ~ subclass(X0,null_class) ),
inference(superposition,[status(thm)],[c_4632,c_53]) ).
tcf(c_4920,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subclass(X0,X3)
| ( sK0(X0,X3) = X2 )
| ( sK0(X0,X3) = X1 )
| ~ subclass(X0,unordered_pair(X1,X2)) ),
inference(superposition,[status(thm)],[c_4591,c_59]) ).
tcf(c_9010,plain,
! [X0: $i] :
( subclass(sK6,X0)
| ( sK0(sK6,X0) = sK7 ) ),
inference(superposition,[status(thm)],[c_130,c_4920]) ).
tcf(c_9603,plain,
( ( null_class = sK6 )
| ( sK0(sK6,null_class) = sK7 ) ),
inference(superposition,[status(thm)],[c_9010,c_4633]) ).
tcf(c_9611,plain,
sK0(sK6,null_class) = sK7,
inference(global_subsumption_just,[status(thm)],[c_9603,c_128,c_9603]) ).
tcf(c_10567,plain,
( member(sK7,sK6)
| subclass(sK6,null_class) ),
inference(superposition,[status(thm)],[c_9611,c_50]) ).
tcf(c_10574,plain,
subclass(sK6,null_class),
inference(global_subsumption_just,[status(thm)],[c_10567,c_129,c_1894,c_3523,c_10567]) ).
tcf(c_10586,plain,
null_class = sK6,
inference(superposition,[status(thm)],[c_10574,c_4633]) ).
tcf(c_10588,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_10586,c_128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET096+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n013.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
% 0.09/0.36 % DateTime : Thu Sep 24 09:45:21 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.39 Running first-order theorem proving
% 0.03/0.39 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
% 0.03/0.41
% 0.03/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.41
% 0.03/0.41 % Detected problem language: tptp
% 0.03/0.42 % Proving...
% 65.45/9.94 % SZS status Started for theBenchmark.p
% 65.45/9.94 % SZS status Theorem for theBenchmark.p
% 65.45/9.94
% 65.45/9.94 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 65.45/9.94
% 65.45/9.94 % ------ iProver source info
% 65.45/9.94
% 65.45/9.94 % git: date: 2026-07-19 20:42:38 +0200
% 65.45/9.94 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 65.45/9.94 % git: non_committed_changes: false
% 65.45/9.94
% 65.45/9.94 % ------ Parsing...
% 65.45/9.94 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 65.45/9.94
% 65.45/9.94 % ------ 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 %
% 65.45/9.94
% 65.45/9.94 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 65.45/9.94
% 65.45/9.94 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 65.45/9.94 % ------ Proving...
% 65.45/9.94 % ------ Problem Properties
% 65.45/9.94
% 65.45/9.94 %
% 65.45/9.94 % clauses 77
% 65.45/9.94 % conjectures 3
% 65.45/9.94 % EPR 8
% 65.45/9.94 % Horn 69
% 65.45/9.94 % unary 17
% 65.45/9.94 % binary 39
% 65.45/9.94 % lits 159
% 65.45/9.94 % lits eq 16
% 65.45/9.94 % fd_pure 0
% 65.45/9.94 % fd_pseudo 0
% 65.45/9.94 % fd_cond 4
% 65.45/9.94 % fd_pseudo_cond 3
% 65.45/9.94 % AC symbols 0
% 65.45/9.94
% 65.45/9.94 % ------ Input Options Time Limit: Unbounded
% 65.45/9.94
% 65.45/9.94
% 65.45/9.94 % ------
% 65.45/9.94 % Current options:
% 65.45/9.94 % ------
% 65.45/9.94
% 65.45/9.94
% 65.45/9.94 %
% 65.45/9.94
% 65.45/9.94 % ------ Proving...
% 65.45/9.94 %
% 65.45/9.94
% 65.45/9.94 % SZS status Theorem for theBenchmark.p
% 65.45/9.94
% 65.45/9.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 65.45/9.94
% 65.45/9.94
%------------------------------------------------------------------------------