%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM011-1 : 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 : 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 02:23:13 PM UTC 2026
% Result : Unsatisfiable 3.67s 1.55s
% Output : CNFRefutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 30 ( 14 unt; 0 def)
% Number of atoms : 50 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 23 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 37 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( little_set(X0)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',a2) ).
fof(f6,axiom,
! [X2,X0,X1] :
( X0 != X1
| ~ little_set(X0)
| member(X0,non_ordered_pair(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair2) ).
fof(f9,axiom,
! [X0] : singleton_set(X0) = non_ordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',singleton_set) ).
fof(f35,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',intersection2) ).
fof(f37,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',complement1) ).
fof(f38,axiom,
! [X0,X1] :
( member(X0,X1)
| ~ little_set(X0)
| member(X0,complement(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',complement2) ).
fof(f39,axiom,
! [X0,X1] : union(X0,X1) = complement(intersection(complement(X0),complement(X1))),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',union) ).
fof(f69,axiom,
! [X0] : successor(X0) = union(X0,singleton_set(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',successor) ).
fof(f70,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',empty_set) ).
fof(f247,axiom,
member(f75,natural_numbers),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_natural_number) ).
fof(f248,negated_conjecture,
empty_set = successor(f75),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_zero_is_first) ).
fof(f249,plain,
! [X0] : successor(X0) = complement(intersection(complement(X0),complement(non_ordered_pair(X0,X0)))),
inference(definition_unfolding,[],[f69,f39,f9]) ).
fof(f317,plain,
empty_set = complement(intersection(complement(f75),complement(non_ordered_pair(f75,f75)))),
inference(definition_unfolding,[],[f248,f249]) ).
fof(f318,plain,
! [X2,X1] :
( ~ little_set(X1)
| member(X1,non_ordered_pair(X1,X2)) ),
inference(equality_resolution,[],[f6]) ).
tcf(c_270,plain,
! [X0: $i,X1: $i] :
( little_set(X0)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_275,plain,
! [X0: $i,X1: $i] :
( member(X0,non_ordered_pair(X0,X1))
| ~ little_set(X0) ),
inference(cnf_transformation,[],[f318]) ).
tcf(c_296,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_298,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_299,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ little_set(X0) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_323,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f70]) ).
tcf(c_483,plain,
member(f75,natural_numbers),
inference(cnf_transformation,[],[f247]) ).
tcf(c_484,negated_conjecture,
complement(intersection(complement(f75),complement(non_ordered_pair(f75,f75)))) = empty_set,
inference(cnf_transformation,[],[f317]) ).
tcf(c_549,plain,
! [X0: $i] :
( member(X0,empty_set)
| member(X0,intersection(complement(f75),complement(non_ordered_pair(f75,f75))))
| ~ little_set(X0) ),
inference(superposition,[status(thm)],[c_484,c_299]) ).
tcf(c_568,plain,
! [X0: $i] :
( ~ little_set(X0)
| member(X0,intersection(complement(f75),complement(non_ordered_pair(f75,f75)))) ),
inference(global_subsumption_just,[status(thm)],[c_549,c_323,c_549]) ).
tcf(c_569,plain,
! [X0: $i] :
( member(X0,intersection(complement(f75),complement(non_ordered_pair(f75,f75))))
| ~ little_set(X0) ),
inference(renaming,[status(thm)],[c_568]) ).
tcf(c_576,plain,
! [X0: $i] :
( member(X0,complement(non_ordered_pair(f75,f75)))
| ~ little_set(X0) ),
inference(superposition,[status(thm)],[c_569,c_296]) ).
tcf(c_589,plain,
! [X0: $i] :
( ~ little_set(X0)
| ~ member(X0,non_ordered_pair(f75,f75)) ),
inference(superposition,[status(thm)],[c_576,c_298]) ).
tcf(c_599,plain,
~ little_set(f75),
inference(superposition,[status(thm)],[c_275,c_589]) ).
tcf(c_745,plain,
little_set(f75),
inference(superposition,[status(thm)],[c_483,c_270]) ).
tcf(c_747,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_745,c_599]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM011-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.19/0.45 % Computer : n003.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Thu Sep 24 02:40:21 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.46 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 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
% 0.24/0.54
% 0.24/0.54 % ======== iProver multi-core TPTP/SMT =========
% 0.24/0.54
% 0.24/0.54 % Detected problem language: tptp
% 0.24/0.56 % Proving...
% 3.67/1.55 % SZS status Started for theBenchmark.p
% 3.67/1.55 % SZS status Unsatisfiable for theBenchmark.p
% 3.67/1.55
% 3.67/1.55 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.67/1.55
% 3.67/1.55 % ------ iProver source info
% 3.67/1.55
% 3.67/1.55 % git: date: 2026-07-19 20:42:38 +0200
% 3.67/1.55 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.67/1.55 % git: non_committed_changes: false
% 3.67/1.55
% 3.67/1.55 % ------ Parsing...% successful
% 3.67/1.55
% 3.67/1.55
% 3.67/1.55 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.67/1.55 % ------ Proving...
% 3.67/1.55 % ------ Problem Properties
% 3.67/1.55
% 3.67/1.55 %
% 3.67/1.55 % clauses 215
% 3.67/1.55 % conjectures 1
% 3.67/1.55 % EPR 34
% 3.67/1.55 % Horn 156
% 3.67/1.55 % unary 10
% 3.67/1.55 % binary 118
% 3.67/1.55 % lits 613
% 3.67/1.55 % lits eq 51
% 3.67/1.55 % fd_pure 0
% 3.67/1.55 % fd_pseudo 0
% 3.67/1.55 % fd_cond 7
% 3.67/1.55 % fd_pseudo_cond 9
% 3.67/1.55 % AC symbols 0
% 3.67/1.55
% 3.67/1.55 % ------ Input Options Time Limit: Unbounded
% 3.67/1.55
% 3.67/1.55
% 3.67/1.55 % ------
% 3.67/1.55 % Current options:
% 3.67/1.55 % ------
% 3.67/1.55
% 3.67/1.55
% 3.67/1.55 %
% 3.67/1.55
% 3.67/1.55 % ------ Proving...
% 3.67/1.55 %
% 3.67/1.55
% 3.67/1.55 % ------ Proving...
% 3.67/1.55 %
% 3.67/1.55
% 3.67/1.55 % ------ Proving...
% 3.67/1.55 %
% 3.67/1.55
% 3.67/1.55 % SZS status Unsatisfiable for theBenchmark.p
% 3.67/1.55
% 3.67/1.55 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.67/1.55
% 3.67/1.55
%------------------------------------------------------------------------------