%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET366+4 : 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 : n016.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 02:47:10 PM UTC 2026
% Result : Theorem 2.50s 1.27s
% Output : CNFRefutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 14 unt; 1 def)
% Number of atoms : 58 ( 1 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 52 ( 24 ~; 17 |; 7 &)
% ( 3 <=>; 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 : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 34 !; 3 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f3,axiom,
! [X0,X1] :
( member(X0,power_set(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',power_set) ).
fof(f6,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(f12,conjecture,
! [X0] : member(empty_set,power_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI47) ).
fof(f13,negated_conjecture,
~ ! [X0] : member(empty_set,power_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] : ~ member(empty_set,power_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(f20,plain,
! [X0,X1] :
( ( ~ member(X0,power_set(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| member(X0,power_set(X1)) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f36,plain,
~ member(empty_set,power_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(f41,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f48,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f63,plain,
~ member(empty_set,power_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_52,plain,
! [X0: $i,X1: $i] :
( member(X0,power_set(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_60,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f48]) ).
tcf(c_75,negated_conjecture,
~ member(empty_set,power_set(sK3)),
inference(cnf_transformation,[],[f63]) ).
tcf(c_471,definition,
iPr_def_10 = power_set(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_472,negated_conjecture,
~ member(empty_set,iPr_def_10),
inference(demodulation,[status(thm)],[c_75,c_471]) ).
tcf(c_970,plain,
! [X0: $i] : subset(empty_set,X0),
inference(superposition,[status(thm)],[c_50,c_60]) ).
tcf(c_981,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ subset(X0,sK3) ),
inference(superposition,[status(thm)],[c_471,c_52]) ).
tcf(c_1020,plain,
member(empty_set,iPr_def_10),
inference(superposition,[status(thm)],[c_970,c_981]) ).
tcf(c_1022,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1020,c_472]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET366+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 10:48:27 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 2.50/1.27 % SZS status Started for theBenchmark.p
% 2.50/1.27 % SZS status Theorem for theBenchmark.p
% 2.50/1.27
% 2.50/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.50/1.27
% 2.50/1.27 % ------ iProver source info
% 2.50/1.27
% 2.50/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.50/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.50/1.27 % git: non_committed_changes: false
% 2.50/1.27
% 2.50/1.27 % ------ Parsing...
% 2.50/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.50/1.27
% 2.50/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.50/1.27
% 2.50/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.50/1.27
% 2.50/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.50/1.27 % ------ Proving...
% 2.50/1.27 % ------ Problem Properties
% 2.50/1.27
% 2.50/1.27 %
% 2.50/1.27 % clauses 28
% 2.50/1.27 % conjectures 1
% 2.50/1.27 % EPR 3
% 2.50/1.27 % Horn 23
% 2.50/1.27 % unary 6
% 2.50/1.27 % binary 15
% 2.50/1.27 % lits 57
% 2.50/1.27 % lits eq 4
% 2.50/1.27 % fd_pure 0
% 2.50/1.27 % fd_pseudo 0
% 2.50/1.27 % fd_cond 0
% 2.50/1.27 % fd_pseudo_cond 2
% 2.50/1.27 % AC symbols 0
% 2.50/1.27
% 2.50/1.27 % ------ Schedule dynamic 5 is on
% 2.50/1.27
% 2.50/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.50/1.27
% 2.50/1.27
% 2.50/1.27 % ------
% 2.50/1.27 % Current options:
% 2.50/1.27 % ------
% 2.50/1.27
% 2.50/1.27
% 2.50/1.27 %
% 2.50/1.27
% 2.50/1.27 % ------ Proving...
% 2.50/1.27 %
% 2.50/1.27
% 2.50/1.27 % SZS status Theorem for theBenchmark.p
% 2.50/1.27
% 2.50/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.50/1.27
% 2.50/1.27
%------------------------------------------------------------------------------