%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN375+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 : 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 03:39:53 PM UTC 2026
% Result : Theorem 1.66s 11.30s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 30 ( 1 unt; 0 def)
% Number of atoms : 127 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 159 ( 62 ~; 70 |; 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 : 73 ( 0 sgn 51 !; 22 ?; 14 :)
% 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',x2126) ).
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)
| big_p(sK6) )
& ( ! [X12] : ~ big_p(X12)
| big_p(X11) ) )
| ( ( ~ big_p(sK5)
| big_p(sK4) )
& ( ! [X8] : ~ big_p(X8)
| ! [X7] : big_p(X7) ) ) )
& ( ( ( big_p(sK2)
| big_p(sK3) )
& ( ~ big_p(sK2)
| ! [X5] : ~ big_p(X5) ) )
| ( ( ! [X3] : big_p(X3)
| big_p(sK1) )
& ( ~ big_p(sK0)
| ! [X0] : ~ big_p(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X1,sK0),skolemize(X2,sK1),skolemize(X4,sK2),skolemize(X6,sK3),skolemize(X9,sK4),skolemize(X10,sK5),skolemize(X13,sK6)],[f6]) ).
fof(f11,plain,
! [X11,X8,X7,X12] :
( ~ big_p(X12)
| big_p(X11)
| ~ big_p(X8)
| big_p(X7) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X3] :
( big_p(sK2)
| big_p(sK3)
| big_p(X3)
| big_p(sK1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f14,plain,
! [X0] :
( big_p(sK2)
| big_p(sK3)
| ~ big_p(sK0)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X0,X5] :
( ~ big_p(sK2)
| ~ big_p(X5)
| ~ big_p(sK0)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ big_p(sK2)
| ~ big_p(sK0)
| ~ big_p(X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_50,negated_conjecture,
! [X0: $i] :
( big_p(sK3)
| big_p(sK2)
| ~ big_p(sK0)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_52,negated_conjecture,
! [X0: $i] :
( big_p(sK1)
| big_p(sK3)
| big_p(sK2)
| big_p(X0) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_53,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,[],[f11]) ).
tcf(c_59,plain,
( ~ big_p(sK2)
| ~ big_p(sK0) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_62,plain,
! [X0: $i] :
( big_p(sK3)
| ~ big_p(X0)
| ~ big_p(sK0) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_50,c_59]) ).
tcf(c_63,negated_conjecture,
! [X0: $i] :
( big_p(sK3)
| ~ big_p(sK0)
| ~ big_p(X0) ),
inference(renaming,[status(thm)],[c_62]) ).
tcf(c_114,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ~ big_p(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_63]) ).
tcf(c_116,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| big_p(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_53]) ).
tcf(c_117,negated_conjecture,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_53]) ).
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_10
| ~ big_p(X0) ),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_126,negated_conjecture,
! [X0: $i] :
( big_p(X0)
| ~ iPr_def_11 ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_127,plain,
( big_p(sK2)
| ~ iPr_def_11 ),
inference(instantiation,[status(thm)],[c_126]) ).
tcf(c_128,plain,
( ~ iPr_def_10
| ~ big_p(sK2) ),
inference(instantiation,[status(thm)],[c_125]) ).
tcf(c_129,plain,
( ~ iPr_def_10
| ~ big_p(sK1) ),
inference(instantiation,[status(thm)],[c_125]) ).
tcf(c_130,plain,
( big_p(sK0)
| ~ iPr_def_11 ),
inference(instantiation,[status(thm)],[c_126]) ).
tcf(c_132,plain,
( ~ iPr_def_10
| ~ big_p(sK3) ),
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_125,c_127,c_122,c_59,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN375+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/10.38 % Computer : n013.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Fri Sep 25 01:01:07 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/10.42 Running first-order theorem proving
% 0.14/10.42 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
% 0.14/10.44
% 0.14/10.44 % ======== iProver multi-core TPTP/SMT =========
% 0.14/10.44
% 0.14/10.44 % Detected problem language: tptp
% 0.14/10.45 % Proving...
% 1.66/11.30 % SZS status Started for theBenchmark.p
% 1.66/11.30 % SZS status Theorem for theBenchmark.p
% 1.66/11.30
% 1.66/11.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.66/11.30
% 1.66/11.30 % ------ iProver source info
% 1.66/11.30
% 1.66/11.30 % git: date: 2026-07-19 20:42:38 +0200
% 1.66/11.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.66/11.30 % git: non_committed_changes: false
% 1.66/11.30
% 1.66/11.30 % ------ Parsing...
% 1.66/11.30 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 1.66/11.30 %
% 1.66/11.30
% 1.66/11.30 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.66/11.30
% 1.66/11.30 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 1.66/11.30 gs_s sp: 5 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.66/11.30 % ------ Proving...
% 1.66/11.30 % ------ Problem Properties
% 1.66/11.30
% 1.66/11.30 %
% 1.66/11.30 % clauses 6
% 1.66/11.30 % conjectures 6
% 1.66/11.30 % EPR 6
% 1.66/11.30 % Horn 3
% 1.66/11.30 % unary 0
% 1.66/11.30 % binary 4
% 1.66/11.30 % lits 14
% 1.66/11.30 % lits eq 0
% 1.66/11.30 % fd_pure 0
% 1.66/11.30 % fd_pseudo 0
% 1.66/11.30 % fd_cond 0
% 1.66/11.30 % fd_pseudo_cond 0
% 1.66/11.30 % AC symbols 0
% 1.66/11.30
% 1.66/11.30 % ------ Schedule EPR non Horn non eq is on
% 1.66/11.30
% 1.66/11.30 % ------ no equalities: superposition off
% 1.66/11.30
% 1.66/11.30 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 1.66/11.30
% 1.66/11.30
% 1.66/11.30 % ------
% 1.66/11.30 % Current options:
% 1.66/11.30 % ------
% 1.66/11.30
% 1.66/11.30
% 1.66/11.30 %
% 1.66/11.30
% 1.66/11.30 % ------ Proving...
% 1.66/11.30 %
% 1.66/11.30
% 1.66/11.30 % SZS status Theorem for theBenchmark.p
% 1.66/11.30
% 1.66/11.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.66/11.30
% 1.66/11.30
%------------------------------------------------------------------------------