%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET062+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.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 02:46:19 PM UTC 2026
% Result : Theorem 0.69s 1.08s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 11 unt; 0 def)
% Number of atoms : 39 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 39 ( 18 ~; 12 |; 6 &)
% ( 2 <=>; 1 =>; 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 : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 24 !; 3 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f5,conjecture,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_empty_set_subset) ).
fof(f6,negated_conjecture,
~ ! [X0] : subset(empty_set,X0),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f8,plain,
? [X0] : ~ subset(empty_set,X0),
inference(ennf_transformation,[],[f6]) ).
fof(f9,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK0(X0,X1),X0)
& ~ member(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f10]) ).
fof(f12,plain,
~ subset(empty_set,sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f8]) ).
fof(f13,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f1]) ).
fof(f15,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f18,plain,
~ subset(empty_set,sK1),
inference(cnf_transformation,[],[f12]) ).
tcf(c_49,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f13]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_54,negated_conjecture,
~ subset(empty_set,sK1),
inference(cnf_transformation,[],[f18]) ).
tcf(c_97,plain,
member(sK0(empty_set,sK1),empty_set),
inference(resolution,[status(thm)],[c_51,c_54]) ).
tcf(c_100,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_97,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET062+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.32 % Computer : n012.cluster.edu
% 0.03/0.32 % Model : x86_64 x86_64
% 0.03/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.32 % Memory : 8046.5625MB
% 0.03/0.32 % OS : Linux 6.8.0-71-generic
% 0.03/0.32 % CPULimit : 300
% 0.03/0.32 % WCLimit : 300
% 0.03/0.32 % DateTime : Thu Sep 24 09:29:56 UTC 2026
% 0.03/0.32 % CPUTime :
% 0.03/0.32 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 Running first-order theorem proving
% 0.08/0.34 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
% 0.08/0.35
% 0.08/0.35 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.35
% 0.08/0.35 % Detected problem language: tptp
% 0.08/0.35 % Proving...
% 0.69/1.08 % SZS status Started for theBenchmark.p
% 0.69/1.08 % SZS status Theorem for theBenchmark.p
% 0.69/1.08
% 0.69/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.69/1.08
% 0.69/1.08 % ------ iProver source info
% 0.69/1.08
% 0.69/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 0.69/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.69/1.08 % git: non_committed_changes: false
% 0.69/1.08
% 0.69/1.08 % ------ Parsing...
% 0.69/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.69/1.08
% 0.69/1.08 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s %
% 0.69/1.08
% 0.69/1.08 % SZS status Theorem for theBenchmark.p
% 0.69/1.08
% 0.69/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.69/1.08
% 0.69/1.08
%------------------------------------------------------------------------------