%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET044+1 : TPTP v9.3.1. Released v2.0.0.
% 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 02:46:14 PM UTC 2026
% Result : Theorem 1.42s 1.15s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 27 ( 1 unt; 0 def)
% Number of atoms : 77 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 88 ( 38 ~; 32 |; 10 &)
% ( 6 <=>; 2 =>; 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 : 50 ( 0 sgn 40 !; 10 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X0] :
! [X1] :
( element(X1,X0)
<=> element(X1,X1) )
=> ~ ! [X2] :
? [X3] :
! [X4] :
( element(X4,X3)
<=> ~ element(X4,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel40) ).
fof(f2,negated_conjecture,
~ ( ? [X0] :
! [X1] :
( element(X1,X0)
<=> element(X1,X1) )
=> ~ ! [X2] :
? [X3] :
! [X4] :
( element(X4,X3)
<=> ~ element(X4,X2) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ? [X0] :
! [X1] :
( element(X1,X0)
<=> element(X1,X1) )
& ! [X2] :
? [X3] :
! [X4] :
( element(X4,X3)
<=> ~ element(X4,X2) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ? [X0] :
! [X1] :
( ( ~ element(X1,X0)
| element(X1,X1) )
& ( ~ element(X1,X1)
| element(X1,X0) ) )
& ! [X2] :
? [X3] :
! [X4] :
( ( ~ element(X4,X3)
| ~ element(X4,X2) )
& ( element(X4,X2)
| element(X4,X3) ) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f5,plain,
( ? [X3] :
! [X4] :
( ( ~ element(X4,X3)
| element(X4,X4) )
& ( ~ element(X4,X4)
| element(X4,X3) ) )
& ! [X0] :
? [X1] :
! [X2] :
( ( ~ element(X2,X1)
| ~ element(X2,X0) )
& ( element(X2,X0)
| element(X2,X1) ) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
( ! [X4] :
( ( ~ element(X4,sK1)
| element(X4,X4) )
& ( ~ element(X4,X4)
| element(X4,sK1) ) )
& ! [X0,X2] :
( ( ~ element(X2,sK0(X0))
| ~ element(X2,X0) )
& ( element(X2,X0)
| element(X2,sK0(X0)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0(X0)),skolemize(X3,sK1)],[f5]) ).
fof(f7,plain,
! [X4] :
( ~ element(X4,sK1)
| element(X4,X4) ),
inference(cnf_transformation,[],[f6]) ).
fof(f8,plain,
! [X4] :
( ~ element(X4,X4)
| element(X4,sK1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f9,plain,
! [X2,X0] :
( ~ element(X2,sK0(X0))
| ~ element(X2,X0) ),
inference(cnf_transformation,[],[f6]) ).
fof(f10,plain,
! [X2,X0] :
( element(X2,X0)
| element(X2,sK0(X0)) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i] :
( element(X0,X1)
| element(X0,sK0(X1)) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_50,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ element(X0,X1)
| ~ element(X0,sK0(X1)) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] :
( element(X0,sK1)
| ~ element(X0,X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_52,negated_conjecture,
! [X0: $i] :
( element(X0,X0)
| ~ element(X0,sK1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_91,negated_conjecture,
! [X0: $i] :
( element(X0,X0)
| ~ element(X0,sK1) ),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_92,negated_conjecture,
! [X0: $i] :
( element(X0,sK1)
| ~ element(X0,X0) ),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_93,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ element(X0,X1)
| ~ element(X0,sK0(X1)) ),
inference(demodulation,[status(thm)],[c_50]) ).
tcf(c_94,negated_conjecture,
! [X0: $i,X1: $i] :
( element(X0,X1)
| element(X0,sK0(X1)) ),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_95,plain,
! [X0: $i] :
( ~ element(sK0(X0),X0)
| ~ element(sK0(X0),sK0(X0)) ),
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_96,plain,
! [X0: $i] :
( element(sK0(X0),sK0(X0))
| ~ element(sK0(X0),sK1) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_97,plain,
( ~ element(sK0(sK1),sK1)
| ~ element(sK0(sK1),sK0(sK1)) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_98,plain,
( element(sK0(sK1),sK0(sK1))
| ~ element(sK0(sK1),sK1) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_102,plain,
! [X0: $i] :
( element(sK0(X0),X0)
| element(sK0(X0),sK0(X0)) ),
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_103,plain,
! [X0: $i] :
( element(sK0(X0),sK1)
| ~ element(sK0(X0),sK0(X0)) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_104,plain,
( element(sK0(sK1),sK1)
| element(sK0(sK1),sK0(sK1)) ),
inference(instantiation,[status(thm)],[c_102]) ).
tcf(c_105,plain,
( element(sK0(sK1),sK1)
| ~ element(sK0(sK1),sK0(sK1)) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_110,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_105,c_104,c_98,c_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET044+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.34 % Computer : n018.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Thu Sep 24 09:27:03 UTC 2026
% 0.10/0.34 % CPUTime :
% 0.10/0.34 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 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
% 0.13/0.39
% 0.13/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.39
% 0.13/0.39 % Detected problem language: tptp
% 0.13/0.40 % Proving...
% 1.42/1.15 % SZS status Started for theBenchmark.p
% 1.42/1.15 % SZS status Theorem for theBenchmark.p
% 1.42/1.15
% 1.42/1.15 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.42/1.15
% 1.42/1.15 % ------ iProver source info
% 1.42/1.15
% 1.42/1.15 % git: date: 2026-07-19 20:42:38 +0200
% 1.42/1.15 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.42/1.15 % git: non_committed_changes: false
% 1.42/1.15
% 1.42/1.15 % ------ Parsing...
% 1.42/1.15 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.42/1.15
% 1.42/1.15 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.42/1.15
% 1.42/1.15 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.42/1.15 % ------ Proving...
% 1.42/1.15 % ------ Problem Properties
% 1.42/1.15
% 1.42/1.15 %
% 1.42/1.15 % clauses 4
% 1.42/1.15 % conjectures 4
% 1.42/1.15 % EPR 2
% 1.42/1.15 % Horn 3
% 1.42/1.15 % unary 0
% 1.42/1.15 % binary 4
% 1.42/1.15 % lits 8
% 1.42/1.15 % lits eq 0
% 1.42/1.15 % fd_pure 0
% 1.42/1.15 % fd_pseudo 0
% 1.42/1.15 % fd_cond 0
% 1.42/1.15 % fd_pseudo_cond 0
% 1.42/1.15 % AC symbols 0
% 1.42/1.15
% 1.42/1.15 % ------ Schedule dynamic 5 is on
% 1.42/1.15
% 1.42/1.15 % ------ no equalities: superposition off
% 1.42/1.15
% 1.42/1.15 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.42/1.15
% 1.42/1.15
% 1.42/1.15 % ------
% 1.42/1.15 % Current options:
% 1.42/1.15 % ------
% 1.42/1.15
% 1.42/1.15
% 1.42/1.15 %
% 1.42/1.15
% 1.42/1.15 % ------ Proving...
% 1.42/1.15 %
% 1.42/1.15
% 1.42/1.15 % SZS status Theorem for theBenchmark.p
% 1.42/1.15
% 1.42/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.42/1.15
% 1.42/1.15
%------------------------------------------------------------------------------