%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN966+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n008.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 03:45:32 PM UTC 2026
% Result : Theorem 1.53s 1.24s
% Output : CNFRefutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 26 ( 6 unt; 0 def)
% Number of atoms : 96 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 113 ( 43 ~; 43 |; 17 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% 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 : 55 ( 0 sgn 47 !; 8 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0,X1] :
( eq(X0,X1)
<=> ! [X2] :
( a_member_of(X2,X0)
<=> a_member_of(X2,X1) ) )
=> ! [X3,X4] :
( eq(X3,X4)
=> eq(X4,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f2,negated_conjecture,
~ ( ! [X0,X1] :
( eq(X0,X1)
<=> ! [X2] :
( a_member_of(X2,X0)
<=> a_member_of(X2,X1) ) )
=> ! [X3,X4] :
( eq(X3,X4)
=> eq(X4,X3) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X0,X1] :
( eq(X0,X1)
<=> ! [X2] :
( a_member_of(X2,X0)
<=> a_member_of(X2,X1) ) )
& ? [X3,X4] :
( eq(X3,X4)
& ~ eq(X4,X3) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ! [X0,X1] :
( ( ~ eq(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) ) )
| eq(X0,X1) ) )
& ? [X3,X4] :
( eq(X3,X4)
& ~ eq(X4,X3) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f5,plain,
( ! [X2,X3] :
( ( ~ eq(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) ) )
| eq(X2,X3) ) )
& ? [X0,X1] :
( eq(X0,X1)
& ~ eq(X1,X0) ) ),
inference(rectify,[],[f4]) ).
fof(f6,plain,
( ! [X2,X3] :
( ( ~ eq(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) ) )
| eq(X2,X3) ) )
& eq(sK0,sK1)
& ~ eq(sK1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X4,sK2(X2,X3))],[f5]) ).
fof(f7,plain,
! [X2,X3,X5] :
( ~ eq(X2,X3)
| ~ a_member_of(X5,X2)
| a_member_of(X5,X3) ),
inference(cnf_transformation,[],[f6]) ).
fof(f8,plain,
! [X2,X3,X5] :
( ~ eq(X2,X3)
| ~ a_member_of(X5,X3)
| a_member_of(X5,X2) ),
inference(cnf_transformation,[],[f6]) ).
fof(f9,plain,
! [X2,X3] :
( a_member_of(sK2(X2,X3),X2)
| a_member_of(sK2(X2,X3),X3)
| eq(X2,X3) ),
inference(cnf_transformation,[],[f6]) ).
fof(f10,plain,
! [X2,X3] :
( ~ a_member_of(sK2(X2,X3),X2)
| ~ a_member_of(sK2(X2,X3),X3)
| eq(X2,X3) ),
inference(cnf_transformation,[],[f6]) ).
fof(f11,plain,
eq(sK0,sK1),
inference(cnf_transformation,[],[f6]) ).
fof(f12,plain,
~ eq(sK1,sK0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_49,negated_conjecture,
~ eq(sK1,sK0),
inference(cnf_transformation,[],[f12]) ).
tcf(c_50,negated_conjecture,
eq(sK0,sK1),
inference(cnf_transformation,[],[f11]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i] :
( eq(X0,X1)
| ~ a_member_of(sK2(X0,X1),X1)
| ~ a_member_of(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i] :
( eq(X0,X1)
| a_member_of(sK2(X0,X1),X1)
| a_member_of(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( a_member_of(X2,X0)
| ~ a_member_of(X2,X1)
| ~ eq(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_54,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( a_member_of(X2,X1)
| ~ a_member_of(X2,X0)
| ~ eq(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_137,plain,
( a_member_of(sK2(sK1,sK0),sK0)
| a_member_of(sK2(sK1,sK0),sK1) ),
inference(resolution,[status(thm)],[c_49,c_52]) ).
tcf(c_144,plain,
( ~ a_member_of(sK2(sK1,sK0),sK0)
| ~ a_member_of(sK2(sK1,sK0),sK1) ),
inference(resolution,[status(thm)],[c_49,c_51]) ).
tcf(c_151,plain,
! [X0: $i] :
( a_member_of(X0,sK1)
| ~ a_member_of(X0,sK0) ),
inference(resolution,[status(thm)],[c_50,c_54]) ).
tcf(c_158,plain,
a_member_of(sK2(sK1,sK0),sK1),
inference(backward_subsumption_resolution,[status(thm)],[c_137,c_151]) ).
tcf(c_192,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( a_member_of(X2,X0)
| ~ a_member_of(X2,X1)
| ~ eq(X0,X1) ),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_199,plain,
! [X0: $i] :
( a_member_of(sK2(sK1,sK0),X0)
| ~ eq(X0,sK1)
| ~ a_member_of(sK2(sK1,sK0),sK1) ),
inference(instantiation,[status(thm)],[c_192]) ).
tcf(c_200,plain,
( a_member_of(sK2(sK1,sK0),sK0)
| ~ eq(sK0,sK1)
| ~ a_member_of(sK2(sK1,sK0),sK1) ),
inference(instantiation,[status(thm)],[c_199]) ).
tcf(c_201,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_200,c_158,c_144,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN966+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.43 % Computer : n008.cluster.edu
% 0.09/0.43 % Model : x86_64 x86_64
% 0.09/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.43 % Memory : 8046.5625MB
% 0.09/0.43 % OS : Linux 6.8.0-71-generic
% 0.09/0.43 % CPULimit : 300
% 0.09/0.43 % WCLimit : 300
% 0.09/0.43 % DateTime : Fri Sep 25 02:41:25 UTC 2026
% 0.09/0.43 % CPUTime :
% 0.09/0.43 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.47 Running first-order theorem proving
% 0.13/0.47 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
% 0.13/0.48
% 0.13/0.48 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.48
% 0.13/0.49 % Detected problem language: tptp
% 0.13/0.50 % Proving...
% 1.53/1.24 % SZS status Started for theBenchmark.p
% 1.53/1.24 % SZS status Theorem for theBenchmark.p
% 1.53/1.24
% 1.53/1.24 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.53/1.24
% 1.53/1.24 % ------ iProver source info
% 1.53/1.24
% 1.53/1.24 % git: date: 2026-07-19 20:42:38 +0200
% 1.53/1.24 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.53/1.24 % git: non_committed_changes: false
% 1.53/1.24
% 1.53/1.24 % ------ Parsing...
% 1.53/1.24 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.53/1.24
% 1.53/1.24 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.53/1.24
% 1.53/1.24 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.53/1.24 % ------ Proving...
% 1.53/1.24 % ------ Problem Properties
% 1.53/1.24
% 1.53/1.24 %
% 1.53/1.24 % clauses 6
% 1.53/1.24 % conjectures 6
% 1.53/1.24 % EPR 4
% 1.53/1.24 % Horn 5
% 1.53/1.24 % unary 2
% 1.53/1.24 % binary 0
% 1.53/1.24 % lits 14
% 1.53/1.24 % lits eq 0
% 1.53/1.24 % fd_pure 0
% 1.53/1.24 % fd_pseudo 0
% 1.53/1.24 % fd_cond 0
% 1.53/1.24 % fd_pseudo_cond 0
% 1.53/1.24 % AC symbols 0
% 1.53/1.24
% 1.53/1.24 % ------ Schedule dynamic 5 is on
% 1.53/1.24
% 1.53/1.24 % ------ no equalities: superposition off
% 1.53/1.24
% 1.53/1.24 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.53/1.24
% 1.53/1.24
% 1.53/1.24 % ------
% 1.53/1.24 % Current options:
% 1.53/1.24 % ------
% 1.53/1.24
% 1.53/1.24
% 1.53/1.24 %
% 1.53/1.24
% 1.53/1.24 % ------ Proving...
% 1.53/1.24 %
% 1.53/1.24
% 1.53/1.24 % SZS status Theorem for theBenchmark.p
% 1.53/1.24
% 1.53/1.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.53/1.24
% 1.53/1.24
%------------------------------------------------------------------------------