%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET788+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 02:48:35 PM UTC 2026
% Result : Theorem 1.70s 1.27s
% Output : CNFRefutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 37 ( 1 unt; 0 def)
% Number of atoms : 146 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 176 ( 67 ~; 78 |; 16 &)
% ( 11 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 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 : 71 ( 0 sgn 63 !; 8 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0,X1] :
( equalish(X0,X1)
<=> ! [X2] :
( a_member_of(X2,X0)
<=> a_member_of(X2,X1) ) )
=> ! [X0,X1] :
( equalish(X0,X1)
<=> equalish(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f2,negated_conjecture,
~ ( ! [X0,X1] :
( equalish(X0,X1)
<=> ! [X2] :
( a_member_of(X2,X0)
<=> a_member_of(X2,X1) ) )
=> ! [X0,X1] :
( equalish(X0,X1)
<=> equalish(X1,X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ! [X0,X1] :
( equalish(X0,X1)
<=> ! [X2] :
( a_member_of(X2,X0)
<=> a_member_of(X2,X1) ) )
=> ! [X3,X4] :
( equalish(X3,X4)
<=> equalish(X4,X3) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ! [X0,X1] :
( equalish(X0,X1)
<=> ! [X2] :
( a_member_of(X2,X0)
<=> a_member_of(X2,X1) ) )
& ? [X3,X4] :
( equalish(X3,X4)
<~> equalish(X4,X3) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ! [X0,X1] :
( ( ~ equalish(X0,X1)
| ! [X2] :
( ( ~ a_member_of(X2,X0)
| a_member_of(X2,X1) )
& ( ~ a_member_of(X2,X1)
| a_member_of(X2,X0) ) ) )
& ( ? [X2] :
( ( a_member_of(X2,X0)
| a_member_of(X2,X1) )
& ( ~ a_member_of(X2,X0)
| ~ a_member_of(X2,X1) ) )
| equalish(X0,X1) ) )
& ? [X3,X4] :
( ( equalish(X3,X4)
| equalish(X4,X3) )
& ( ~ equalish(X3,X4)
| ~ equalish(X4,X3) ) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
( ! [X2,X3] :
( ( ~ equalish(X2,X3)
| ! [X5] :
( ( ~ a_member_of(X5,X2)
| a_member_of(X5,X3) )
& ( ~ a_member_of(X5,X3)
| a_member_of(X5,X2) ) ) )
& ( ? [X4] :
( ( a_member_of(X4,X2)
| a_member_of(X4,X3) )
& ( ~ a_member_of(X4,X2)
| ~ a_member_of(X4,X3) ) )
| equalish(X2,X3) ) )
& ? [X0,X1] :
( ( equalish(X0,X1)
| equalish(X1,X0) )
& ( ~ equalish(X0,X1)
| ~ equalish(X1,X0) ) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ! [X2,X3] :
( ( ~ equalish(X2,X3)
| ! [X5] :
( ( ~ a_member_of(X5,X2)
| a_member_of(X5,X3) )
& ( ~ a_member_of(X5,X3)
| a_member_of(X5,X2) ) ) )
& ( ( ( a_member_of(sK2(X2,X3),X2)
| a_member_of(sK2(X2,X3),X3) )
& ( ~ a_member_of(sK2(X2,X3),X2)
| ~ a_member_of(sK2(X2,X3),X3) ) )
| equalish(X2,X3) ) )
& ( equalish(sK0,sK1)
| equalish(sK1,sK0) )
& ( ~ equalish(sK0,sK1)
| ~ equalish(sK1,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X4,sK2(X2,X3))],[f6]) ).
fof(f8,plain,
! [X2,X3,X5] :
( ~ equalish(X2,X3)
| ~ a_member_of(X5,X2)
| a_member_of(X5,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X2,X3,X5] :
( ~ equalish(X2,X3)
| ~ a_member_of(X5,X3)
| a_member_of(X5,X2) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X2,X3] :
( a_member_of(sK2(X2,X3),X2)
| a_member_of(sK2(X2,X3),X3)
| equalish(X2,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X2,X3] :
( ~ a_member_of(sK2(X2,X3),X2)
| ~ a_member_of(sK2(X2,X3),X3)
| equalish(X2,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
( equalish(sK0,sK1)
| equalish(sK1,sK0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
( ~ equalish(sK0,sK1)
| ~ equalish(sK1,sK0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_49,negated_conjecture,
( ~ equalish(sK0,sK1)
| ~ equalish(sK1,sK0) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_50,negated_conjecture,
( equalish(sK0,sK1)
| equalish(sK1,sK0) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i] :
( equalish(X0,X1)
| ~ a_member_of(sK2(X0,X1),X1)
| ~ a_member_of(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i] :
( equalish(X0,X1)
| a_member_of(sK2(X0,X1),X1)
| a_member_of(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( a_member_of(X2,X0)
| ~ a_member_of(X2,X1)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_54,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( a_member_of(X2,X1)
| ~ a_member_of(X2,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_109,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( a_member_of(X2,X1)
| ~ a_member_of(X2,X0)
| ~ equalish(X0,X1) ),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_110,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( a_member_of(X2,X0)
| ~ a_member_of(X2,X1)
| ~ equalish(X0,X1) ),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_111,negated_conjecture,
! [X0: $i,X1: $i] :
( equalish(X0,X1)
| a_member_of(sK2(X0,X1),X1)
| a_member_of(sK2(X0,X1),X0) ),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_112,negated_conjecture,
! [X0: $i,X1: $i] :
( equalish(X0,X1)
| ~ a_member_of(sK2(X0,X1),X1)
| ~ a_member_of(sK2(X0,X1),X0) ),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_115,plain,
( equalish(sK0,sK1)
| a_member_of(sK2(sK0,sK1),sK0)
| a_member_of(sK2(sK0,sK1),sK1) ),
inference(instantiation,[status(thm)],[c_111]) ).
tcf(c_116,plain,
( equalish(sK0,sK1)
| ~ a_member_of(sK2(sK0,sK1),sK0)
| ~ a_member_of(sK2(sK0,sK1),sK1) ),
inference(instantiation,[status(thm)],[c_112]) ).
tcf(c_119,plain,
! [X0: $i] :
( a_member_of(sK2(sK0,sK1),X0)
| ~ equalish(sK1,X0)
| ~ a_member_of(sK2(sK0,sK1),sK1) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_120,plain,
( a_member_of(sK2(sK0,sK1),sK0)
| ~ equalish(sK1,sK0)
| ~ a_member_of(sK2(sK0,sK1),sK1) ),
inference(instantiation,[status(thm)],[c_119]) ).
tcf(c_121,plain,
( equalish(sK1,sK0)
| ~ a_member_of(sK2(sK1,sK0),sK0)
| ~ a_member_of(sK2(sK1,sK0),sK1) ),
inference(instantiation,[status(thm)],[c_112]) ).
tcf(c_122,plain,
( equalish(sK1,sK0)
| a_member_of(sK2(sK1,sK0),sK0)
| a_member_of(sK2(sK1,sK0),sK1) ),
inference(instantiation,[status(thm)],[c_111]) ).
tcf(c_125,plain,
! [X0: $i] :
( a_member_of(sK2(sK0,sK1),X0)
| ~ equalish(X0,sK0)
| ~ a_member_of(sK2(sK0,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_135,plain,
( a_member_of(sK2(sK0,sK1),sK1)
| ~ equalish(sK1,sK0)
| ~ a_member_of(sK2(sK0,sK1),sK0) ),
inference(instantiation,[status(thm)],[c_125]) ).
tcf(c_149,plain,
! [X0: $i] :
( a_member_of(sK2(sK1,sK0),X0)
| ~ equalish(X0,sK1)
| ~ a_member_of(sK2(sK1,sK0),sK1) ),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_150,plain,
( a_member_of(sK2(sK1,sK0),sK0)
| ~ equalish(sK0,sK1)
| ~ a_member_of(sK2(sK1,sK0),sK1) ),
inference(instantiation,[status(thm)],[c_149]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i] :
( a_member_of(sK2(sK1,sK0),X1)
| ~ equalish(X0,X1)
| ~ a_member_of(sK2(sK1,sK0),X0) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_173,plain,
! [X0: $i] :
( a_member_of(sK2(sK1,sK0),sK1)
| ~ equalish(X0,sK1)
| ~ a_member_of(sK2(sK1,sK0),X0) ),
inference(instantiation,[status(thm)],[c_160]) ).
tcf(c_174,plain,
( a_member_of(sK2(sK1,sK0),sK1)
| ~ equalish(sK0,sK1)
| ~ a_member_of(sK2(sK1,sK0),sK0) ),
inference(instantiation,[status(thm)],[c_173]) ).
tcf(c_175,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_174,c_150,c_135,c_121,c_122,c_120,c_116,c_115,c_49,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET788+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 11:58:13 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 1.70/1.27 % SZS status Started for theBenchmark.p
% 1.70/1.27 % SZS status Theorem for theBenchmark.p
% 1.70/1.27
% 1.70/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.70/1.27
% 1.70/1.27 % ------ iProver source info
% 1.70/1.27
% 1.70/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.70/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.70/1.27 % git: non_committed_changes: false
% 1.70/1.27
% 1.70/1.27 % ------ Parsing...
% 1.70/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.70/1.27
% 1.70/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.70/1.27
% 1.70/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.70/1.27 % ------ Proving...
% 1.70/1.27 % ------ Problem Properties
% 1.70/1.27
% 1.70/1.27 %
% 1.70/1.27 % clauses 6
% 1.70/1.27 % conjectures 6
% 1.70/1.27 % EPR 4
% 1.70/1.27 % Horn 4
% 1.70/1.27 % unary 0
% 1.70/1.27 % binary 2
% 1.70/1.27 % lits 16
% 1.70/1.27 % lits eq 0
% 1.70/1.27 % fd_pure 0
% 1.70/1.27 % fd_pseudo 0
% 1.70/1.27 % fd_cond 0
% 1.70/1.27 % fd_pseudo_cond 0
% 1.70/1.27 % AC symbols 0
% 1.70/1.27
% 1.70/1.27 % ------ Schedule dynamic 5 is on
% 1.70/1.27
% 1.70/1.27 % ------ no equalities: superposition off
% 1.70/1.27
% 1.70/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.70/1.27
% 1.70/1.27
% 1.70/1.27 % ------
% 1.70/1.27 % Current options:
% 1.70/1.27 % ------
% 1.70/1.27
% 1.70/1.27
% 1.70/1.27 %
% 1.70/1.27
% 1.70/1.27 % ------ Proving...
% 1.70/1.27 %
% 1.70/1.27
% 1.70/1.27 % SZS status Theorem for theBenchmark.p
% 1.70/1.27
% 1.70/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.70/1.27
% 1.70/1.27
%------------------------------------------------------------------------------