%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN374+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 : n018.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 1.47s 1.17s
% Output : CNFRefutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 35 ( 1 unt; 0 def)
% Number of atoms : 144 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 172 ( 63 ~; 82 |; 15 &)
% ( 11 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 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 : 5 ( 4 usr; 4 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 74 ( 0 sgn 54 !; 20 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) )
<=> ( ? [X0] : big_p(X0)
<=> ! [X1] : big_p(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2125) ).
fof(f2,negated_conjecture,
~ ( ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) )
<=> ( ? [X0] : big_p(X0)
<=> ! [X1] : big_p(X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
~ ( ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) )
<=> ( ? [X2] : big_p(X2)
<=> ! [X3] : big_p(X3) ) ),
inference(rectify,[],[f2]) ).
fof(f4,plain,
( ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) )
<~> ( ? [X2] : big_p(X2)
<=> ! [X3] : big_p(X3) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
( ( ? [X0] :
! [X1] :
( ( ~ big_p(X0)
| big_p(X1) )
& ( ~ big_p(X1)
| big_p(X0) ) )
| ( ( ! [X2] : ~ big_p(X2)
| ! [X3] : big_p(X3) )
& ( ? [X3] : ~ big_p(X3)
| ? [X2] : big_p(X2) ) ) )
& ( ! [X0] :
? [X1] :
( ( big_p(X0)
| big_p(X1) )
& ( ~ big_p(X0)
| ~ 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,
( ( ? [X10] :
! [X11] :
( ( ~ big_p(X10)
| big_p(X11) )
& ( ~ big_p(X11)
| big_p(X10) ) )
| ( ( ! [X9] : ~ big_p(X9)
| ! [X8] : big_p(X8) )
& ( ? [X7] : ~ big_p(X7)
| ? [X6] : big_p(X6) ) ) )
& ( ! [X4] :
? [X5] :
( ( big_p(X4)
| big_p(X5) )
& ( ~ big_p(X4)
| ~ 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(sK5)
| big_p(X11) )
& ( ~ big_p(X11)
| big_p(sK5) ) )
| ( ( ! [X9] : ~ big_p(X9)
| ! [X8] : big_p(X8) )
& ( ~ big_p(sK4)
| big_p(sK3) ) ) )
& ( ! [X4] :
( ( big_p(X4)
| big_p(sK2(X4)) )
& ( ~ big_p(X4)
| ~ big_p(sK2(X4)) ) )
| ( ( 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]),skolemize(X0,sK0),skolemize(X3,sK1),skolemize(X5,sK2(X4)),skolemize(X6,sK3),skolemize(X7,sK4),skolemize(X10,sK5)],[f6]) ).
fof(f8,plain,
! [X11,X8,X9] :
( ~ big_p(sK5)
| big_p(X11)
| ~ big_p(X9)
| big_p(X8) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X11,X8,X9] :
( ~ big_p(X11)
| big_p(sK5)
| ~ big_p(X9)
| big_p(X8) ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X2,X4] :
( big_p(X4)
| big_p(sK2(X4))
| big_p(sK1)
| big_p(X2) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X1,X4] :
( ~ big_p(X4)
| ~ big_p(sK2(X4))
| ~ big_p(X1)
| ~ big_p(sK0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ big_p(sK0)
| ~ big_p(X1)
| ~ big_p(X0)
| ~ big_p(sK2(X0)) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i] :
( big_p(sK1)
| big_p(X1)
| big_p(X0)
| big_p(sK2(X0)) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_55,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_p(sK5)
| big_p(X2)
| ~ big_p(X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_56,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( big_p(X2)
| big_p(X1)
| ~ big_p(sK5)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_58,plain,
( ~ big_p(sK5)
| ~ big_p(sK0)
| ~ big_p(sK2(sK5)) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_155,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| big_p(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_56]) ).
tcf(c_156,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ~ big_p(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_56]) ).
tcf(c_157,negated_conjecture,
( iPr_def_11
| iPr_def_10
| ~ big_p(sK5) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_56]) ).
tcf(c_158,negated_conjecture,
( iPr_def_11
| iPr_def_10
| big_p(sK5) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_55]) ).
tcf(c_159,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| big_p(sK2(X0))
| big_p(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_52]) ).
tcf(c_160,negated_conjecture,
( iPr_def_12
| iPr_def_10
| big_p(sK1) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_52]) ).
tcf(c_165,negated_conjecture,
( iPr_def_11
| iPr_def_10
| ~ big_p(sK5) ),
inference(demodulation,[status(thm)],[c_157]) ).
tcf(c_169,negated_conjecture,
( iPr_def_11
| iPr_def_10
| big_p(sK5) ),
inference(demodulation,[status(thm)],[c_158]) ).
tcf(c_173,negated_conjecture,
( iPr_def_12
| iPr_def_10
| big_p(sK1) ),
inference(demodulation,[status(thm)],[c_160]) ).
tcf(c_178,negated_conjecture,
! [X0: $i] :
( big_p(X0)
| ~ iPr_def_10 ),
inference(demodulation,[status(thm)],[c_155]) ).
tcf(c_181,negated_conjecture,
! [X0: $i] :
( big_p(X0)
| big_p(sK2(X0))
| ~ iPr_def_12 ),
inference(demodulation,[status(thm)],[c_159]) ).
tcf(c_184,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ~ big_p(X0) ),
inference(demodulation,[status(thm)],[c_156]) ).
tcf(c_185,plain,
( big_p(sK5)
| ~ iPr_def_10 ),
inference(instantiation,[status(thm)],[c_178]) ).
tcf(c_189,plain,
( big_p(sK0)
| ~ iPr_def_10 ),
inference(instantiation,[status(thm)],[c_178]) ).
tcf(c_191,plain,
! [X0: $i] :
( big_p(sK2(X0))
| ~ iPr_def_10 ),
inference(instantiation,[status(thm)],[c_178]) ).
tcf(c_192,plain,
( big_p(sK2(sK5))
| ~ iPr_def_10 ),
inference(instantiation,[status(thm)],[c_191]) ).
tcf(c_195,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ big_p(sK2(X0)) ),
inference(instantiation,[status(thm)],[c_184]) ).
tcf(c_203,plain,
( ~ iPr_def_11
| ~ big_p(sK1) ),
inference(instantiation,[status(thm)],[c_184]) ).
tcf(c_204,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_203,c_195,c_192,c_189,c_181,c_165,c_184,c_185,c_178,c_173,c_169,c_58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN374+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 01:03:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.42
% 0.14/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.42
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 1.47/1.17 % SZS status Started for theBenchmark.p
% 1.47/1.17 % SZS status Theorem for theBenchmark.p
% 1.47/1.17
% 1.47/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.47/1.17
% 1.47/1.17 % ------ iProver source info
% 1.47/1.17
% 1.47/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 1.47/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.47/1.17 % git: non_committed_changes: false
% 1.47/1.17
% 1.47/1.17 % ------ Parsing...
% 1.47/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.47/1.17
% 1.47/1.17 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.47/1.17
% 1.47/1.17 % ------ Preprocessing... gs_s sp: 14 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.47/1.17 % ------ Proving...
% 1.47/1.17 % ------ Problem Properties
% 1.47/1.17
% 1.47/1.17 %
% 1.47/1.17 % clauses 10
% 1.47/1.17 % conjectures 10
% 1.47/1.17 % EPR 8
% 1.47/1.17 % Horn 3
% 1.47/1.17 % unary 0
% 1.47/1.17 % binary 2
% 1.47/1.17 % lits 28
% 1.47/1.17 % lits eq 0
% 1.47/1.17 % fd_pure 0
% 1.47/1.17 % fd_pseudo 0
% 1.47/1.17 % fd_cond 0
% 1.47/1.17 % fd_pseudo_cond 0
% 1.47/1.17 % AC symbols 0
% 1.47/1.17
% 1.47/1.17 % ------ Schedule dynamic 5 is on
% 1.47/1.17
% 1.47/1.17 % ------ no equalities: superposition off
% 1.47/1.17
% 1.47/1.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.47/1.17
% 1.47/1.17
% 1.47/1.17 % ------
% 1.47/1.17 % Current options:
% 1.47/1.17 % ------
% 1.47/1.17
% 1.47/1.17
% 1.47/1.17 %
% 1.47/1.17
% 1.47/1.17 % ------ Proving...
% 1.47/1.17 %
% 1.47/1.17
% 1.47/1.17 % SZS status Theorem for theBenchmark.p
% 1.47/1.17
% 1.47/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.47/1.17
% 1.47/1.17
%------------------------------------------------------------------------------