%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN377+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 : n019.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 03:39:54 PM UTC 2026
% Result : Theorem 1.56s 1.27s
% Output : CNFRefutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 29 ( 1 unt; 0 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 151 ( 56 ~; 68 |; 15 &)
% ( 11 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 72 ( 0 sgn 54 !; 18 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
( big_p(X0)
<=> ! [X1] : big_p(X1) )
<=> ( ? [X0] : big_p(X0)
<=> ! [X1] : big_p(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2128) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( big_p(X0)
<=> ! [X1] : big_p(X1) )
<=> ( ? [X0] : big_p(X0)
<=> ! [X1] : big_p(X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ! [X0] :
( big_p(X0)
<=> ! [X1] : big_p(X1) )
<=> ( ? [X2] : big_p(X2)
<=> ! [X3] : big_p(X3) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ! [X0] :
( big_p(X0)
<=> ! [X1] : big_p(X1) )
<~> ( ? [X2] : big_p(X2)
<=> ! [X3] : big_p(X3) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ! [X0] :
( ( ~ big_p(X0)
| ! [X1] : big_p(X1) )
& ( ? [X1] : ~ big_p(X1)
| big_p(X0) ) )
| ( ( ! [X2] : ~ big_p(X2)
| ! [X3] : big_p(X3) )
& ( ? [X3] : ~ big_p(X3)
| ? [X2] : big_p(X2) ) ) )
& ( ? [X0] :
( ( big_p(X0)
| ! [X1] : big_p(X1) )
& ( ~ big_p(X0)
| ? [X1] : ~ big_p(X1) ) )
| ( ( ? [X2] : big_p(X2)
| ! [X3] : big_p(X3) )
& ( ! [X2] : ~ big_p(X2)
| ? [X3] : ~ big_p(X3) ) ) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
( ( ! [X11] :
( ( ~ big_p(X11)
| ! [X13] : big_p(X13) )
& ( ? [X12] : ~ big_p(X12)
| big_p(X11) ) )
| ( ( ! [X10] : ~ big_p(X10)
| ! [X9] : big_p(X9) )
& ( ? [X8] : ~ big_p(X8)
| ? [X7] : big_p(X7) ) ) )
& ( ? [X4] :
( ( big_p(X4)
| ! [X6] : big_p(X6) )
& ( ~ big_p(X4)
| ? [X5] : ~ big_p(X5) ) )
| ( ( ? [X3] : big_p(X3)
| ! [X2] : big_p(X2) )
& ( ! [X1] : ~ big_p(X1)
| ? [X0] : ~ big_p(X0) ) ) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
( ( ! [X11] :
( ( ~ big_p(X11)
| ! [X13] : big_p(X13) )
& ( ~ big_p(sK6)
| big_p(X11) ) )
| ( ( ! [X10] : ~ big_p(X10)
| ! [X9] : big_p(X9) )
& ( ~ big_p(sK5)
| big_p(sK4) ) ) )
& ( ( ( big_p(sK2)
| ! [X6] : big_p(X6) )
& ( ~ big_p(sK2)
| ~ big_p(sK3) ) )
| ( ( big_p(sK1)
| ! [X2] : big_p(X2) )
& ( ! [X1] : ~ big_p(X1)
| ~ big_p(sK0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X3,sK1),skolemize(X4,sK2),skolemize(X5,sK3),skolemize(X7,sK4),skolemize(X8,sK5),skolemize(X12,sK6)],[f6]) ).
fof(f8,plain,
! [X10,X11,X9,X13] :
( ~ big_p(X11)
| big_p(X13)
| ~ big_p(X10)
| big_p(X9) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X2,X6] :
( big_p(sK2)
| big_p(X6)
| big_p(sK1)
| big_p(X2) ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X2] :
( ~ big_p(sK2)
| ~ big_p(sK3)
| big_p(sK1)
| big_p(X2) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X1] :
( ~ big_p(sK2)
| ~ big_p(sK3)
| ~ big_p(X1)
| ~ big_p(sK0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] :
( ~ big_p(sK2)
| ~ big_p(sK3)
| ~ big_p(sK0)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] :
( big_p(sK1)
| big_p(X0)
| ~ big_p(sK2)
| ~ big_p(sK3) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i] :
( big_p(sK1)
| big_p(sK2)
| big_p(X1)
| big_p(X0) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_56,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( big_p(X3)
| big_p(X2)
| ~ big_p(X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_57,plain,
( big_p(sK1)
| big_p(sK2) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_62,negated_conjecture,
! [X0: $i] :
( big_p(sK1)
| big_p(X0)
| ~ big_p(sK3) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_57,c_51]) ).
tcf(c_114,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| big_p(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_62]) ).
tcf(c_116,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ~ big_p(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_56]) ).
tcf(c_117,negated_conjecture,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_56]) ).
tcf(c_122,negated_conjecture,
( iPr_def_11
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_125,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ~ big_p(X0) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_126,negated_conjecture,
! [X0: $i] :
( big_p(X0)
| ~ iPr_def_10 ),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_127,plain,
( big_p(sK2)
| ~ iPr_def_10 ),
inference(instantiation,[status(thm)],[c_126]) ).
tcf(c_128,plain,
( ~ iPr_def_11
| ~ big_p(sK2) ),
inference(instantiation,[status(thm)],[c_125]) ).
tcf(c_129,plain,
( big_p(sK3)
| ~ iPr_def_10 ),
inference(instantiation,[status(thm)],[c_126]) ).
tcf(c_130,plain,
( big_p(sK0)
| ~ iPr_def_10 ),
inference(instantiation,[status(thm)],[c_126]) ).
tcf(c_132,plain,
( ~ iPr_def_11
| ~ big_p(sK1) ),
inference(instantiation,[status(thm)],[c_125]) ).
tcf(c_133,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_132,c_130,c_129,c_128,c_127,c_126,c_122,c_49,c_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN377+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 01:01:49 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.40 Running first-order theorem proving
% 0.16/0.40 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
% 0.16/0.41
% 0.16/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.41
% 0.16/0.41 % Detected problem language: tptp
% 0.16/0.42 % Proving...
% 1.56/1.27 % SZS status Started for theBenchmark.p
% 1.56/1.27 % SZS status Theorem for theBenchmark.p
% 1.56/1.27
% 1.56/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.56/1.27
% 1.56/1.27 % ------ iProver source info
% 1.56/1.27
% 1.56/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.56/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.56/1.27 % git: non_committed_changes: false
% 1.56/1.27
% 1.56/1.27 % ------ Parsing...
% 1.56/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 1.56/1.27 %
% 1.56/1.27
% 1.56/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.56/1.27
% 1.56/1.27 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 1.56/1.27 gs_s sp: 5 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.56/1.27 % ------ Proving...
% 1.56/1.27 % ------ Problem Properties
% 1.56/1.27
% 1.56/1.27 %
% 1.56/1.27 % clauses 6
% 1.56/1.27 % conjectures 6
% 1.56/1.27 % EPR 6
% 1.56/1.27 % Horn 3
% 1.56/1.27 % unary 0
% 1.56/1.27 % binary 4
% 1.56/1.27 % lits 14
% 1.56/1.27 % lits eq 0
% 1.56/1.27 % fd_pure 0
% 1.56/1.27 % fd_pseudo 0
% 1.56/1.27 % fd_cond 0
% 1.56/1.27 % fd_pseudo_cond 0
% 1.56/1.27 % AC symbols 0
% 1.56/1.27
% 1.56/1.27 % ------ Schedule EPR non Horn non eq is on
% 1.56/1.27
% 1.56/1.27 % ------ no equalities: superposition off
% 1.56/1.27
% 1.56/1.27 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 1.56/1.27
% 1.56/1.27
% 1.56/1.27 % ------
% 1.56/1.27 % Current options:
% 1.56/1.27 % ------
% 1.56/1.27
% 1.56/1.27
% 1.56/1.27 %
% 1.56/1.27
% 1.56/1.27 % ------ Proving...
% 1.56/1.27 %
% 1.56/1.27
% 1.56/1.27 % SZS status Theorem for theBenchmark.p
% 1.56/1.27
% 1.56/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.56/1.27
% 1.56/1.27
%------------------------------------------------------------------------------