%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET044-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n013.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 : Unsatisfiable 1.59s 1.34s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 1 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 40 ( 20 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 22 ( 0 sgn 22 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] :
( element(X0,X0)
| ~ element(X0,a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
fof(f2,negated_conjecture,
! [X0] :
( element(X0,a)
| ~ element(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
fof(f3,negated_conjecture,
! [X0,X1] :
( ~ element(X0,X1)
| ~ element(X0,f(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
fof(f4,negated_conjecture,
! [X0,X1] :
( element(X0,f(X1))
| element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
tcf(c_53,negated_conjecture,
! [X0: $i] :
( element(X0,X0)
| ~ element(X0,a) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_54,negated_conjecture,
! [X0: $i] :
( element(X0,a)
| ~ element(X0,X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_55,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ element(X0,X1)
| ~ element(X0,f(X1)) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_56,negated_conjecture,
! [X0: $i,X1: $i] :
( element(X0,X1)
| element(X0,f(X1)) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_95,negated_conjecture,
! [X0: $i,X1: $i] :
( element(X0,X1)
| element(X0,f(X1)) ),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_96,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ element(X0,X1)
| ~ element(X0,f(X1)) ),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_97,negated_conjecture,
! [X0: $i] :
( element(X0,a)
| ~ element(X0,X0) ),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_98,negated_conjecture,
! [X0: $i] :
( element(X0,X0)
| ~ element(X0,a) ),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_99,plain,
! [X0: $i] :
( element(f(X0),X0)
| element(f(X0),f(X0)) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_100,plain,
! [X0: $i] :
( element(f(X0),a)
| ~ element(f(X0),f(X0)) ),
inference(instantiation,[status(thm)],[c_97]) ).
tcf(c_101,plain,
( element(f(a),a)
| element(f(a),f(a)) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_102,plain,
( element(f(a),a)
| ~ element(f(a),f(a)) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_105,plain,
! [X0: $i] :
( element(f(X0),f(X0))
| ~ element(f(X0),a) ),
inference(instantiation,[status(thm)],[c_98]) ).
tcf(c_106,plain,
( element(f(a),f(a))
| ~ element(f(a),a) ),
inference(instantiation,[status(thm)],[c_105]) ).
tcf(c_107,plain,
! [X0: $i] :
( ~ element(f(X0),a)
| ~ element(f(X0),f(a)) ),
inference(instantiation,[status(thm)],[c_96]) ).
tcf(c_108,plain,
( ~ element(f(a),a)
| ~ element(f(a),f(a)) ),
inference(instantiation,[status(thm)],[c_107]) ).
tcf(c_112,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_108,c_106,c_102,c_101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET044-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.43 % Computer : n013.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Thu Sep 24 09:24:51 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.47 Running first-order theorem proving
% 0.18/0.47 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
% 0.18/0.48
% 0.18/0.48 % ======== iProver multi-core TPTP/SMT =========
% 0.18/0.48
% 0.18/0.49 % Detected problem language: tptp
% 0.23/0.50 % Proving...
% 1.59/1.34 % SZS status Started for theBenchmark.p
% 1.59/1.34 % SZS status Unsatisfiable for theBenchmark.p
% 1.59/1.34
% 1.59/1.34 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.59/1.34
% 1.59/1.34 % ------ iProver source info
% 1.59/1.34
% 1.59/1.34 % git: date: 2026-07-19 20:42:38 +0200
% 1.59/1.34 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.59/1.34 % git: non_committed_changes: false
% 1.59/1.34
% 1.59/1.34 % ------ Parsing...% successful
% 1.59/1.34
% 1.59/1.34
% 1.59/1.34 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.59/1.34
% 1.59/1.34 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.59/1.34
% 1.59/1.34 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.59/1.34 % ------ Proving...
% 1.59/1.34 % ------ Problem Properties
% 1.59/1.34
% 1.59/1.34 %
% 1.59/1.34 % clauses 4
% 1.59/1.34 % conjectures 4
% 1.59/1.34 % EPR 2
% 1.59/1.34 % Horn 3
% 1.59/1.34 % unary 0
% 1.59/1.34 % binary 4
% 1.59/1.34 % lits 8
% 1.59/1.34 % lits eq 0
% 1.59/1.34 % fd_pure 0
% 1.59/1.34 % fd_pseudo 0
% 1.59/1.34 % fd_cond 0
% 1.59/1.34 % fd_pseudo_cond 0
% 1.59/1.34 % AC symbols 0
% 1.59/1.34
% 1.59/1.34 % ------ Schedule dynamic 5 is on
% 1.59/1.34
% 1.59/1.34 % ------ no equalities: superposition off
% 1.59/1.34
% 1.59/1.34 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.59/1.34
% 1.59/1.34
% 1.59/1.34 % ------
% 1.59/1.34 % Current options:
% 1.59/1.34 % ------
% 1.59/1.34
% 1.59/1.34
% 1.59/1.34 %
% 1.59/1.34
% 1.59/1.34 % ------ Proving...
% 1.59/1.34 %
% 1.59/1.34
% 1.59/1.34 % SZS status Unsatisfiable for theBenchmark.p
% 1.59/1.34
% 1.59/1.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.59/1.34
% 1.59/1.34
%------------------------------------------------------------------------------