%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU143+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n014.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 02:55:34 PM UTC 2026
% Result : Theorem 0.43s 1.28s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 15 unt; 1 def)
% Number of atoms : 73 ( 39 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 76 ( 33 ~; 28 |; 12 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 34 !; 5 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f3,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f7,conjecture,
! [X0] : singleton(X0) != empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0] : singleton(X0) != empty_set,
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f12,plain,
? [X0] : singleton(X0) = empty_set,
inference(ennf_transformation,[],[f8]) ).
fof(f13,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| X2 = X0 )
& ( X0 != X2
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f14,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| X2 = X0 )
& ( ~ in(X2,X1)
| X0 != X2 ) )
| X1 = singleton(X0) ) ),
inference(rectify,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( singleton(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| X0 = X3 )
& ( X0 != X3
| in(X3,X1) ) ) )
& ( ( ( in(sK0(X0,X1),X1)
| sK0(X0,X1) = X0 )
& ( ~ in(sK0(X0,X1),X1)
| sK0(X0,X1) != X0 ) )
| X1 = singleton(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f14]) ).
fof(f16,plain,
! [X0] :
( ( empty_set != X0
| ! [X1] : ~ in(X1,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f17,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( ? [X1] : in(X1,X0)
| X0 = empty_set ) ),
inference(rectify,[],[f16]) ).
fof(f18,plain,
! [X0] :
( ( empty_set != X0
| ! [X2] : ~ in(X2,X0) )
& ( in(sK1(X0),X0)
| X0 = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f17]) ).
fof(f19,plain,
empty_set = singleton(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f12]) ).
fof(f24,plain,
! [X3,X0,X1] :
( singleton(X0) != X1
| X0 != X3
| in(X3,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
! [X2,X0] :
( empty_set != X0
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
empty_set = singleton(sK2),
inference(cnf_transformation,[],[f19]) ).
fof(f33,plain,
! [X3,X1] :
( singleton(X3) != X1
| in(X3,X1) ),
inference(equality_resolution,[],[f24]) ).
fof(f34,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f33]) ).
fof(f36,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f27]) ).
tcf(c_52,plain,
! [X0: $i] : in(X0,singleton(X0)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_55,plain,
! [X0: $i] : ~ in(X0,empty_set),
inference(cnf_transformation,[],[f36]) ).
tcf(c_57,negated_conjecture,
singleton(sK2) = empty_set,
inference(cnf_transformation,[],[f30]) ).
tcf(c_140,definition,
iPr_def_10 = singleton(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_141,negated_conjecture,
iPr_def_10 = empty_set,
inference(demodulation,[status(thm)],[c_57,c_140]) ).
tcf(c_282,plain,
! [X0: $i] : ~ in(X0,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_55,c_141]) ).
tcf(c_283,plain,
in(sK2,iPr_def_10),
inference(superposition,[status(thm)],[c_140,c_52]) ).
tcf(c_284,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_283,c_282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU143+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n014.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 12:55:18 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 0.43/1.28 % SZS status Started for theBenchmark.p
% 0.43/1.28 % SZS status Theorem for theBenchmark.p
% 0.43/1.28
% 0.43/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.43/1.28
% 0.43/1.28 % ------ iProver source info
% 0.43/1.28
% 0.43/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 0.43/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.43/1.28 % git: non_committed_changes: false
% 0.43/1.28
% 0.43/1.28 % ------ Parsing...
% 0.43/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.43/1.28
% 0.43/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.43/1.28
% 0.43/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.43/1.28
% 0.43/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.43/1.28 % ------ Proving...
% 0.43/1.28 % ------ Problem Properties
% 0.43/1.28
% 0.43/1.28 %
% 0.43/1.28 % clauses 12
% 0.43/1.28 % conjectures 1
% 0.43/1.28 % EPR 6
% 0.43/1.28 % Horn 10
% 0.43/1.28 % unary 7
% 0.43/1.28 % binary 3
% 0.43/1.28 % lits 19
% 0.43/1.28 % lits eq 8
% 0.43/1.28 % fd_pure 0
% 0.43/1.28 % fd_pseudo 0
% 0.43/1.28 % fd_cond 1
% 0.43/1.28 % fd_pseudo_cond 2
% 0.43/1.28 % AC symbols 0
% 0.43/1.28
% 0.43/1.28 % ------ Schedule dynamic 5 is on
% 0.43/1.28
% 0.43/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.43/1.28
% 0.43/1.28
% 0.43/1.28 % ------
% 0.43/1.28 % Current options:
% 0.43/1.28 % ------
% 0.43/1.28
% 0.43/1.28
% 0.43/1.28 %
% 0.43/1.28
% 0.43/1.28 % ------ Proving...
% 0.43/1.28 %
% 0.43/1.28
% 0.43/1.28 % SZS status Theorem for theBenchmark.p
% 0.43/1.28
% 0.43/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.43/1.28
% 0.43/1.28
%------------------------------------------------------------------------------