%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET786+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n004.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 02:48:34 PM UTC 2026
% Result : Theorem 0.19s 1.24s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 20 ( 2 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 70 ( 32 ~; 25 |; 9 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 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 : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 33 ( 0 sgn 22 !; 11 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ? [X0] :
! [X1] :
( element(X1,X0)
<=> ~ ? [X2] :
( element(X2,X1)
& element(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm25) ).
fof(f2,negated_conjecture,
~ ~ ? [X0] :
! [X1] :
( element(X1,X0)
<=> ~ ? [X2] :
( element(X2,X1)
& element(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0] :
! [X1] :
( element(X1,X0)
<=> ~ ? [X2] :
( element(X2,X1)
& element(X1,X2) ) ),
inference(flattening,[],[f2]) ).
fof(f4,plain,
? [X0] :
! [X1] :
( element(X1,X0)
<=> ! [X2] :
( ~ element(X2,X1)
| ~ element(X1,X2) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
? [X0] :
! [X1] :
( ( ~ element(X1,X0)
| ! [X2] :
( ~ element(X2,X1)
| ~ element(X1,X2) ) )
& ( ? [X2] :
( element(X2,X1)
& element(X1,X2) )
| element(X1,X0) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
? [X0] :
! [X1] :
( ( ~ element(X1,X0)
| ! [X3] :
( ~ element(X3,X1)
| ~ element(X1,X3) ) )
& ( ? [X2] :
( element(X2,X1)
& element(X1,X2) )
| element(X1,X0) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
! [X1] :
( ( ~ element(X1,sK0)
| ! [X3] :
( ~ element(X3,X1)
| ~ element(X1,X3) ) )
& ( ( element(sK1(X1),X1)
& element(X1,sK1(X1)) )
| element(X1,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X2,sK1(X1))],[f6]) ).
fof(f8,plain,
! [X3,X1] :
( ~ element(X1,sK0)
| ~ element(X3,X1)
| ~ element(X1,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X1] :
( element(sK1(X1),X1)
| element(X1,sK0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X1] :
( element(X1,sK1(X1))
| element(X1,sK0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] :
( element(X0,sK0)
| element(X0,sK1(X0)) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_50,negated_conjecture,
! [X0: $i] :
( element(X0,sK0)
| element(sK1(X0),X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ element(X0,sK0)
| ~ element(X1,X0)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_52,plain,
( element(sK0,sK0)
| element(sK1(sK0),sK0) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_53,plain,
( element(sK0,sK0)
| element(sK0,sK1(sK0)) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_54,plain,
~ element(sK0,sK0),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_69,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ element(X0,sK0)
| ~ element(X1,X0)
| ~ element(X0,X1) ),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_72,plain,
! [X0: $i] :
( ~ element(sK1(sK0),sK0)
| ~ element(X0,sK1(sK0))
| ~ element(sK1(sK0),X0) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_74,plain,
( ~ element(sK0,sK1(sK0))
| ~ element(sK1(sK0),sK0) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_75,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_74,c_54,c_53,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET786+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n004.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 11:57:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.38 Running first-order theorem proving
% 0.14/0.38 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
% 0.14/0.39
% 0.14/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.39
% 0.14/0.39 % Detected problem language: tptp
% 0.14/0.40 % Proving...
% 0.19/1.24 % SZS status Started for theBenchmark.p
% 0.19/1.24 % SZS status Theorem for theBenchmark.p
% 0.19/1.24
% 0.19/1.24 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.19/1.24
% 0.19/1.24 % ------ iProver source info
% 0.19/1.24
% 0.19/1.24 % git: date: 2026-07-19 20:42:38 +0200
% 0.19/1.24 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.19/1.24 % git: non_committed_changes: false
% 0.19/1.24
% 0.19/1.24 % ------ Parsing...
% 0.19/1.24 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.19/1.24
% 0.19/1.24 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.19/1.24
% 0.19/1.24 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.19/1.24 % ------ Proving...
% 0.19/1.24 % ------ Problem Properties
% 0.19/1.24
% 0.19/1.24 %
% 0.19/1.24 % clauses 3
% 0.19/1.24 % conjectures 3
% 0.19/1.24 % EPR 1
% 0.19/1.24 % Horn 1
% 0.19/1.24 % unary 0
% 0.19/1.24 % binary 2
% 0.19/1.24 % lits 7
% 0.19/1.24 % lits eq 0
% 0.19/1.24 % fd_pure 0
% 0.19/1.24 % fd_pseudo 0
% 0.19/1.24 % fd_cond 0
% 0.19/1.24 % fd_pseudo_cond 0
% 0.19/1.24 % AC symbols 0
% 0.19/1.24
% 0.19/1.24 % ------ Schedule dynamic 5 is on
% 0.19/1.24
% 0.19/1.24 % ------ no equalities: superposition off
% 0.19/1.24
% 0.19/1.24 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.19/1.24
% 0.19/1.24
% 0.19/1.24 % ------
% 0.19/1.24 % Current options:
% 0.19/1.24 % ------
% 0.19/1.24
% 0.19/1.24
% 0.19/1.24 %
% 0.19/1.24
% 0.19/1.24 % ------ Proving...
% 0.19/1.24 %
% 0.19/1.24
% 0.19/1.24 % SZS status Theorem for theBenchmark.p
% 0.19/1.24
% 0.19/1.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.19/1.24
% 0.19/1.24
%------------------------------------------------------------------------------