%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET047+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n010.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 02:46:15 PM UTC 2026
% Result : Theorem 1.71s 1.27s
% Output : CNFRefutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 35 ( 1 unt; 0 def)
% Number of atoms : 119 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 142 ( 58 ~; 68 |; 11 &)
% ( 4 <=>; 0 =>; 0 <=; 1 <~>)
% 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 : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 42 !; 6 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( set_equal(X0,X1)
<=> ! [X2] :
( element(X2,X0)
<=> element(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel43_1) ).
fof(f2,conjecture,
! [X0,X1] :
( set_equal(X0,X1)
<=> set_equal(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel43) ).
fof(f3,negated_conjecture,
~ ! [X0,X1] :
( set_equal(X0,X1)
<=> set_equal(X1,X0) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
? [X0,X1] :
( set_equal(X0,X1)
<~> set_equal(X1,X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
! [X0,X1] :
( ( ~ set_equal(X0,X1)
| ! [X2] :
( ( ~ element(X2,X0)
| element(X2,X1) )
& ( ~ element(X2,X1)
| element(X2,X0) ) ) )
& ( ? [X2] :
( ( element(X2,X0)
| element(X2,X1) )
& ( ~ element(X2,X0)
| ~ element(X2,X1) ) )
| set_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f6,plain,
! [X0,X1] :
( ( ~ set_equal(X0,X1)
| ! [X3] :
( ( ~ element(X3,X0)
| element(X3,X1) )
& ( ~ element(X3,X1)
| element(X3,X0) ) ) )
& ( ? [X2] :
( ( element(X2,X0)
| element(X2,X1) )
& ( ~ element(X2,X0)
| ~ element(X2,X1) ) )
| set_equal(X0,X1) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( ( ~ set_equal(X0,X1)
| ! [X3] :
( ( ~ element(X3,X0)
| element(X3,X1) )
& ( ~ element(X3,X1)
| element(X3,X0) ) ) )
& ( ( ( element(sK0(X0,X1),X0)
| element(sK0(X0,X1),X1) )
& ( ~ element(sK0(X0,X1),X0)
| ~ element(sK0(X0,X1),X1) ) )
| set_equal(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f6]) ).
fof(f8,plain,
? [X0,X1] :
( ( set_equal(X0,X1)
| set_equal(X1,X0) )
& ( ~ set_equal(X0,X1)
| ~ set_equal(X1,X0) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f9,plain,
( ( set_equal(sK1,sK2)
| set_equal(sK2,sK1) )
& ( ~ set_equal(sK1,sK2)
| ~ set_equal(sK2,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f8]) ).
fof(f10,plain,
! [X3,X0,X1] :
( ~ set_equal(X0,X1)
| ~ element(X3,X0)
| element(X3,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X3,X0,X1] :
( ~ set_equal(X0,X1)
| ~ element(X3,X1)
| element(X3,X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X0,X1] :
( element(sK0(X0,X1),X0)
| element(sK0(X0,X1),X1)
| set_equal(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X0,X1] :
( ~ element(sK0(X0,X1),X0)
| ~ element(sK0(X0,X1),X1)
| set_equal(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
( set_equal(sK1,sK2)
| set_equal(sK2,sK1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f15,plain,
( ~ set_equal(sK1,sK2)
| ~ set_equal(sK2,sK1) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( set_equal(X0,X1)
| ~ element(sK0(X0,X1),X1)
| ~ element(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( set_equal(X0,X1)
| element(sK0(X0,X1),X1)
| element(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X0)
| ~ element(X2,X1)
| ~ set_equal(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( element(X2,X1)
| ~ element(X2,X0)
| ~ set_equal(X0,X1) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_53,negated_conjecture,
( ~ set_equal(sK1,sK2)
| ~ set_equal(sK2,sK1) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_54,negated_conjecture,
( set_equal(sK1,sK2)
| set_equal(sK2,sK1) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_111,plain,
( set_equal(sK1,sK2)
| ~ element(sK0(sK1,sK2),sK1)
| ~ element(sK0(sK1,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_112,plain,
( set_equal(sK1,sK2)
| element(sK0(sK1,sK2),sK1)
| element(sK0(sK1,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_113,plain,
( set_equal(sK2,sK1)
| element(sK0(sK2,sK1),sK1)
| element(sK0(sK2,sK1),sK2) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_114,plain,
( set_equal(sK2,sK1)
| ~ element(sK0(sK2,sK1),sK1)
| ~ element(sK0(sK2,sK1),sK2) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_115,plain,
! [X0: $i] :
( element(sK0(sK2,sK1),X0)
| ~ set_equal(X0,sK2)
| ~ element(sK0(sK2,sK1),sK2) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_116,plain,
( element(sK0(sK2,sK1),sK1)
| ~ set_equal(sK1,sK2)
| ~ element(sK0(sK2,sK1),sK2) ),
inference(instantiation,[status(thm)],[c_115]) ).
tcf(c_123,plain,
! [X0: $i] :
( element(sK0(sK1,sK2),X0)
| ~ set_equal(sK2,X0)
| ~ element(sK0(sK1,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_124,plain,
( element(sK0(sK1,sK2),sK1)
| ~ set_equal(sK2,sK1)
| ~ element(sK0(sK1,sK2),sK2) ),
inference(instantiation,[status(thm)],[c_123]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i] :
( element(sK0(sK1,sK2),X1)
| ~ set_equal(X1,X0)
| ~ element(sK0(sK1,sK2),X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_135,plain,
! [X0: $i] :
( element(sK0(sK1,sK2),sK2)
| ~ set_equal(sK2,X0)
| ~ element(sK0(sK1,sK2),X0) ),
inference(instantiation,[status(thm)],[c_125]) ).
tcf(c_136,plain,
( element(sK0(sK1,sK2),sK2)
| ~ set_equal(sK2,sK1)
| ~ element(sK0(sK1,sK2),sK1) ),
inference(instantiation,[status(thm)],[c_135]) ).
tcf(c_146,plain,
! [X0: $i] :
( element(sK0(sK2,sK1),X0)
| ~ set_equal(sK1,X0)
| ~ element(sK0(sK2,sK1),sK1) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_152,plain,
( element(sK0(sK2,sK1),sK2)
| ~ set_equal(sK1,sK2)
| ~ element(sK0(sK2,sK1),sK1) ),
inference(instantiation,[status(thm)],[c_146]) ).
tcf(c_162,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_152,c_136,c_124,c_116,c_113,c_114,c_112,c_111,c_53,c_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET047+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n010.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 09:26:13 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 1.71/1.27 % SZS status Started for theBenchmark.p
% 1.71/1.27 % SZS status Theorem for theBenchmark.p
% 1.71/1.27
% 1.71/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.71/1.27
% 1.71/1.27 % ------ iProver source info
% 1.71/1.27
% 1.71/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.71/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.71/1.27 % git: non_committed_changes: false
% 1.71/1.27
% 1.71/1.27 % ------ Parsing...
% 1.71/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.71/1.27
% 1.71/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.71/1.27
% 1.71/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.71/1.27 % ------ Proving...
% 1.71/1.27 % ------ Problem Properties
% 1.71/1.27
% 1.71/1.27 %
% 1.71/1.27 % clauses 6
% 1.71/1.27 % conjectures 2
% 1.71/1.27 % EPR 4
% 1.71/1.27 % Horn 4
% 1.71/1.27 % unary 0
% 1.71/1.27 % binary 2
% 1.71/1.27 % lits 16
% 1.71/1.27 % lits eq 0
% 1.71/1.27 % fd_pure 0
% 1.71/1.27 % fd_pseudo 0
% 1.71/1.27 % fd_cond 0
% 1.71/1.27 % fd_pseudo_cond 0
% 1.71/1.27 % AC symbols 0
% 1.71/1.27
% 1.71/1.27 % ------ Schedule dynamic 5 is on
% 1.71/1.27
% 1.71/1.27 % ------ no equalities: superposition off
% 1.71/1.27
% 1.71/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.71/1.27
% 1.71/1.27
% 1.71/1.27 % ------
% 1.71/1.27 % Current options:
% 1.71/1.27 % ------
% 1.71/1.27
% 1.71/1.27
% 1.71/1.27 %
% 1.71/1.27
% 1.71/1.27 % ------ Proving...
% 1.71/1.27 %
% 1.71/1.27
% 1.71/1.27 % SZS status Theorem for theBenchmark.p
% 1.71/1.27
% 1.71/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.71/1.27
% 1.71/1.27
%------------------------------------------------------------------------------