%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET867+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 02:48:51 PM UTC 2026
% Result : Theorem 0.59s 1.36s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 14 unt; 1 def)
% Number of atoms : 93 ( 27 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 103 ( 44 ~; 37 |; 19 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 41 !; 9 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f3,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f7,conjecture,
union(empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_zfmisc_1) ).
fof(f8,negated_conjecture,
union(empty_set) != empty_set,
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
empty_set != union(empty_set),
inference(flattening,[],[f8]) ).
fof(f11,plain,
! [X0] :
( ( empty_set != X0
| ! [X1] : ~ in(X1,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(rectify,[],[f11]) ).
fof(f13,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( in(sK0(X0),X0)
| X0 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f15,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] :
( in(X7,X0)
& in(X5,X7) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] :
( in(X4,X0)
& in(X2,X4) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( in(sK3(X0,X5),X0)
& in(X5,sK3(X0,X5)) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ( ( in(sK1(X0,X1),X1)
| ( in(sK2(X0,X1),X0)
& in(sK1(X0,X1),sK2(X0,X1)) ) )
& ( ~ in(sK1(X0,X1),X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(sK1(X0,X1),X3) ) ) )
| X1 = union(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X4,sK2(X0,X1)),skolemize(X7,sK3(X0,X5))],[f15]) ).
fof(f20,plain,
! [X2,X0] :
( empty_set != X0
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
! [X0] :
( in(sK0(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X0,X1,X5] :
( union(X0) != X1
| ~ in(X5,X1)
| in(sK3(X0,X5),X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
empty_set != union(empty_set),
inference(cnf_transformation,[],[f9]) ).
fof(f32,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f20]) ).
fof(f35,plain,
! [X0,X5] :
( ~ in(X5,union(X0))
| in(sK3(X0,X5),X0) ),
inference(equality_resolution,[],[f22]) ).
tcf(c_50,plain,
! [X0: $i] :
( in(sK0(X0),X0)
| ( X0 = empty_set ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_51,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(cnf_transformation,[],[f32]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( in(sK3(X1,X0),X1)
| ~ in(X0,union(X1)) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_61,negated_conjecture,
union(empty_set) != empty_set,
inference(cnf_transformation,[],[f31]) ).
tcf(c_176,definition,
iPr_def_10 = union(empty_set),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_177,negated_conjecture,
iPr_def_10 != empty_set,
inference(demodulation,[status(thm)],[c_61,c_176]) ).
tcf(c_380,plain,
! [X0: $i] : ~ in(X0,union(empty_set)),
inference(superposition,[status(thm)],[c_57,c_51]) ).
tcf(c_381,plain,
! [X0: $i] : ~ in(X0,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_380,c_176]) ).
tcf(c_443,plain,
empty_set = iPr_def_10,
inference(superposition,[status(thm)],[c_50,c_381]) ).
tcf(c_455,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_177,c_443]) ).
tcf(c_456,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_455]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET867+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.40 % Computer : n018.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Thu Sep 24 12:20:19 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.45 Running first-order theorem proving
% 0.14/0.45 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
% 0.14/0.47
% 0.14/0.47 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.47
% 0.14/0.47 % Detected problem language: tptp
% 0.14/0.49 % Proving...
% 0.59/1.36 % SZS status Started for theBenchmark.p
% 0.59/1.36 % SZS status Theorem for theBenchmark.p
% 0.59/1.36
% 0.59/1.36 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.59/1.36
% 0.59/1.36 % ------ iProver source info
% 0.59/1.36
% 0.59/1.36 % git: date: 2026-07-19 20:42:38 +0200
% 0.59/1.36 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.59/1.36 % git: non_committed_changes: false
% 0.59/1.36
% 0.59/1.36 % ------ Parsing...
% 0.59/1.36 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.59/1.36
% 0.59/1.36 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.59/1.36
% 0.59/1.36 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.59/1.36
% 0.59/1.36 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.59/1.36 % ------ Proving...
% 0.59/1.36 % ------ Problem Properties
% 0.59/1.36
% 0.59/1.36 %
% 0.59/1.36 % clauses 14
% 0.59/1.36 % conjectures 1
% 0.59/1.36 % EPR 6
% 0.59/1.36 % Horn 11
% 0.59/1.36 % unary 6
% 0.59/1.36 % binary 4
% 0.59/1.36 % lits 27
% 0.59/1.36 % lits eq 6
% 0.59/1.36 % fd_pure 0
% 0.59/1.36 % fd_pseudo 0
% 0.59/1.36 % fd_cond 1
% 0.59/1.36 % fd_pseudo_cond 3
% 0.59/1.36 % AC symbols 0
% 0.59/1.36
% 0.59/1.36 % ------ Schedule dynamic 5 is on
% 0.59/1.36
% 0.59/1.36 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.59/1.36
% 0.59/1.36
% 0.59/1.36 % ------
% 0.59/1.36 % Current options:
% 0.59/1.36 % ------
% 0.59/1.36
% 0.59/1.36
% 0.59/1.36 %
% 0.59/1.36
% 0.59/1.36 % ------ Proving...
% 0.59/1.36 %
% 0.59/1.36
% 0.59/1.36 % SZS status Theorem for theBenchmark.p
% 0.59/1.36
% 0.59/1.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.59/1.36
% 0.59/1.36
%------------------------------------------------------------------------------