%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET065+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 : n002.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 02:46:21 PM UTC 2026
% Result : Theorem 2.35s 1.27s
% Output : CNFRefutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 14 unt; 0 def)
% Number of atoms : 79 ( 1 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 79 ( 31 ~; 26 |; 17 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 34 !; 4 ?; 7 :)
% 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(f2,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',class_elements_are_sets) ).
fof(f29,axiom,
! [X0] :
( inductive(X0)
<=> ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SET005+0.ax',infinity) ).
fof(f44,conjecture,
member(null_class,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_is_a_set) ).
fof(f45,negated_conjecture,
~ member(null_class,universal_class),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f46,plain,
~ member(null_class,universal_class),
inference(flattening,[],[f45]) ).
fof(f48,plain,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f52,plain,
? [X0] :
( ! [X1] :
( ~ inductive(X1)
| subclass(X0,X1) )
& inductive(X0)
& member(X0,universal_class) ),
inference(ennf_transformation,[],[f30]) ).
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,[],[f48]) ).
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(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)],[f52]) ).
fof(f103,plain,
! [X3,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f106,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f2]) ).
fof(f159,plain,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f162,plain,
inductive(sK1),
inference(cnf_transformation,[],[f88]) ).
fof(f190,plain,
~ member(null_class,universal_class),
inference(cnf_transformation,[],[f46]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_52,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f106]) ).
tcf(c_98,plain,
! [X0: $i] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_101,plain,
inductive(sK1),
inference(cnf_transformation,[],[f162]) ).
tcf(c_128,negated_conjecture,
~ member(null_class,universal_class),
inference(cnf_transformation,[],[f190]) ).
tcf(c_883,plain,
! [X0: $i] :
( member(null_class,X0)
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_98,c_101]) ).
tcf(c_884,plain,
member(null_class,sK1),
inference(unflattening,[status(thm)],[c_883]) ).
tcf(c_1550,negated_conjecture,
~ member(null_class,universal_class),
inference(demodulation,[status(thm)],[c_128]) ).
tcf(c_2579,plain,
! [X0: $i] :
( member(null_class,X0)
| ~ subclass(sK1,X0) ),
inference(superposition,[status(thm)],[c_884,c_51]) ).
tcf(c_2723,plain,
member(null_class,universal_class),
inference(superposition,[status(thm)],[c_52,c_2579]) ).
tcf(c_2725,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2723,c_1550]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET065+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 09:34:34 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.02/0.40 Running first-order theorem proving
% 0.02/0.40 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
% 0.02/0.41
% 0.02/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.02/0.41
% 0.02/0.41 % Detected problem language: tptp
% 0.02/0.42 % Proving...
% 2.35/1.27 % SZS status Started for theBenchmark.p
% 2.35/1.27 % SZS status Theorem for theBenchmark.p
% 2.35/1.27
% 2.35/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.35/1.27
% 2.35/1.27 % ------ iProver source info
% 2.35/1.27
% 2.35/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.35/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.35/1.27 % git: non_committed_changes: false
% 2.35/1.27
% 2.35/1.27 % ------ Parsing...
% 2.35/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.35/1.27
% 2.35/1.27 % ------ 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 %
% 2.35/1.27
% 2.35/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.35/1.27
% 2.35/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.35/1.27 % ------ Proving...
% 2.35/1.27 % ------ Problem Properties
% 2.35/1.27
% 2.35/1.27 %
% 2.35/1.27 % clauses 75
% 2.35/1.27 % conjectures 1
% 2.35/1.27 % EPR 8
% 2.35/1.27 % Horn 67
% 2.35/1.27 % unary 15
% 2.35/1.27 % binary 39
% 2.35/1.27 % lits 157
% 2.35/1.27 % lits eq 14
% 2.35/1.27 % fd_pure 0
% 2.35/1.27 % fd_pseudo 0
% 2.35/1.27 % fd_cond 4
% 2.35/1.27 % fd_pseudo_cond 3
% 2.35/1.27 % AC symbols 0
% 2.35/1.27
% 2.35/1.27 % ------ Schedule dynamic 5 is on
% 2.35/1.27
% 2.35/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.35/1.27
% 2.35/1.27
% 2.35/1.27 % ------
% 2.35/1.27 % Current options:
% 2.35/1.27 % ------
% 2.35/1.27
% 2.35/1.27
% 2.35/1.27 %
% 2.35/1.27
% 2.35/1.27 % ------ Proving...
% 2.35/1.27 %
% 2.35/1.27
% 2.35/1.27 % SZS status Theorem for theBenchmark.p
% 2.35/1.27
% 2.35/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.35/1.27
% 2.35/1.27
%------------------------------------------------------------------------------