%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET062+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n018.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 1.27s 6.30s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 11 unt; 0 def)
% Number of atoms : 46 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 45 ( 20 ~; 16 |; 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 30 !; 3 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f6,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(f12,conjecture,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI15) ).
fof(f13,negated_conjecture,
~ ! [X0] : subset(empty_set,X0),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f16,plain,
? [X0] : ~ subset(empty_set,X0),
inference(ennf_transformation,[],[f13]) ).
fof(f17,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,[],[f14]) ).
fof(f18,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,[],[f17]) ).
fof(f19,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))],[f18]) ).
fof(f36,plain,
~ subset(empty_set,sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f16]) ).
fof(f38,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f48,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f63,plain,
~ subset(empty_set,sK3),
inference(cnf_transformation,[],[f36]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_60,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f48]) ).
tcf(c_75,negated_conjecture,
~ subset(empty_set,sK3),
inference(cnf_transformation,[],[f63]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_50]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(renaming,[status(thm)],[c_100]) ).
tcf(c_463,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X0)
| ( X1 != sK3 )
| ( X0 != empty_set ) ),
inference(resolution_lifted,[status(thm)],[c_101,c_75]) ).
tcf(c_464,plain,
member(sK0(empty_set,sK3),empty_set),
inference(unflattening,[status(thm)],[c_463]) ).
tcf(c_467,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_464,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET062+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.39 % Computer : n018.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Thu Sep 24 09:32:55 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/5.43 Running first-order theorem proving
% 0.16/5.43 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
% 0.16/5.44
% 0.16/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.44
% 0.16/5.44 % Detected problem language: tptp
% 0.16/5.46 % Proving...
% 1.27/6.30 % SZS status Started for theBenchmark.p
% 1.27/6.30 % SZS status Theorem for theBenchmark.p
% 1.27/6.30
% 1.27/6.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.27/6.30
% 1.27/6.30 % ------ iProver source info
% 1.27/6.30
% 1.27/6.30 % git: date: 2026-07-19 20:42:38 +0200
% 1.27/6.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.27/6.30 % git: non_committed_changes: false
% 1.27/6.30
% 1.27/6.30 % ------ Parsing...
% 1.27/6.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.27/6.30
% 1.27/6.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s %
% 1.27/6.30
% 1.27/6.30 % SZS status Theorem for theBenchmark.p
% 1.27/6.30
% 1.27/6.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.27/6.30
% 1.27/6.30
%------------------------------------------------------------------------------