%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM009-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 02:23:13 PM UTC 2026
% Result : Unsatisfiable 2.73s 1.07s
% Output : CNFRefutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 6 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 10 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 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 : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 8 ( 0 sgn 8 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( little_set(X0)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',a2) ).
fof(f73,axiom,
member(empty_set,infinity),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',infinity2) ).
fof(f190,axiom,
! [X0] :
( member(empty_set,f44(X0))
| ~ little_set(X0)
| member(X0,natural_numbers) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM003-0.ax',natural_numbers4) ).
fof(f192,axiom,
! [X0] :
( ~ member(X0,f44(X0))
| member(X0,natural_numbers) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM003-0.ax',natural_numbers6) ).
fof(f247,negated_conjecture,
~ member(empty_set,natural_numbers),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_zero_is_a_natural) ).
tcf(c_269,plain,
! [X0: $i,X1: $i] :
( little_set(X0)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_325,plain,
member(empty_set,infinity),
inference(cnf_transformation,[],[f73]) ).
tcf(c_431,plain,
! [X0: $i] :
( member(X0,natural_numbers)
| member(empty_set,f44(X0))
| ~ little_set(X0) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_433,plain,
! [X0: $i] :
( member(X0,natural_numbers)
| ~ member(X0,f44(X0)) ),
inference(cnf_transformation,[],[f192]) ).
tcf(c_482,negated_conjecture,
~ member(empty_set,natural_numbers),
inference(cnf_transformation,[],[f247]) ).
tcf(c_569,plain,
( member(empty_set,natural_numbers)
| ~ member(empty_set,f44(empty_set)) ),
inference(instantiation,[status(thm)],[c_433]) ).
tcf(c_609,plain,
( member(empty_set,natural_numbers)
| member(empty_set,f44(empty_set))
| ~ little_set(empty_set) ),
inference(instantiation,[status(thm)],[c_431]) ).
tcf(c_791,plain,
little_set(empty_set),
inference(superposition,[status(thm)],[c_325,c_269]) ).
tcf(c_793,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_791,c_609,c_569,c_482]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM009-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 02:38:45 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 2.73/1.07 % SZS status Started for theBenchmark.p
% 2.73/1.07 % SZS status Unsatisfiable for theBenchmark.p
% 2.73/1.07
% 2.73/1.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.73/1.07
% 2.73/1.07 % ------ iProver source info
% 2.73/1.07
% 2.73/1.07 % git: date: 2026-07-19 20:42:38 +0200
% 2.73/1.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.73/1.07 % git: non_committed_changes: false
% 2.73/1.07
% 2.73/1.07 % ------ Parsing...% successful
% 2.73/1.07
% 2.73/1.07
% 2.73/1.07 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.73/1.07 % ------ Proving...
% 2.73/1.07 % ------ Problem Properties
% 2.73/1.07
% 2.73/1.07 %
% 2.73/1.07 % clauses 214
% 2.73/1.07 % conjectures 1
% 2.73/1.07 % EPR 34
% 2.73/1.07 % Horn 155
% 2.73/1.07 % unary 9
% 2.73/1.07 % binary 118
% 2.73/1.07 % lits 612
% 2.73/1.07 % lits eq 50
% 2.73/1.07 % fd_pure 0
% 2.73/1.07 % fd_pseudo 0
% 2.73/1.07 % fd_cond 7
% 2.73/1.07 % fd_pseudo_cond 9
% 2.73/1.07 % AC symbols 0
% 2.73/1.07
% 2.73/1.07 % ------ Input Options Time Limit: Unbounded
% 2.73/1.07
% 2.73/1.07
% 2.73/1.07 % ------
% 2.73/1.07 % Current options:
% 2.73/1.07 % ------
% 2.73/1.07
% 2.73/1.07
% 2.73/1.07 %
% 2.73/1.07
% 2.73/1.07 % ------ Proving...
% 2.73/1.07 %
% 2.73/1.07
% 2.73/1.07 % ------ Proving...
% 2.73/1.07 %
% 2.73/1.07
% 2.73/1.07 % ------ Proving...
% 2.73/1.07 %
% 2.73/1.07
% 2.73/1.07 % SZS status Unsatisfiable for theBenchmark.p
% 2.73/1.07
% 2.73/1.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.73/1.07
% 2.73/1.07
%------------------------------------------------------------------------------