%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN084+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 : n005.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 03:39:09 PM UTC 2026
% Result : Theorem 1.65s 1.27s
% Output : CNFRefutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 70 ( 10 unt; 4 def)
% Number of atoms : 271 ( 2 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 320 ( 126 ~; 140 |; 43 &)
% ( 4 <=>; 4 =>; 0 <=; 3 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 50 ( 0 sgn 46 !; 4 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
( ( ( big_p(X0)
=> big_p(f(X0)) )
& big_p(a) )
=> big_p(f(f(X0))) )
<=> ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel62) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
( ( ( big_p(X0)
=> big_p(f(X0)) )
& big_p(a) )
=> big_p(f(f(X0))) )
<=> ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X0] :
( ( big_p(X0)
& ~ big_p(f(X0)) )
| ~ big_p(a)
| big_p(f(f(X0))) )
<~> ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
( ! [X0] :
( ( big_p(X0)
& ~ big_p(f(X0)) )
| ~ big_p(a)
| big_p(f(f(X0))) )
<~> ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(flattening,[],[f3]) ).
fof(f8,plain,
( ( ~ sP1
| ! [X0] :
( ( big_p(X0)
& ~ big_p(f(X0)) )
| ~ big_p(a)
| big_p(f(f(X0))) ) )
& ( ? [X0] :
( ( ~ big_p(X0)
| big_p(f(X0)) )
& big_p(a)
& ~ big_p(f(f(X0))) )
| sP1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f9,plain,
( ( ~ sP1
| ! [X1] :
( ( big_p(X1)
& ~ big_p(f(X1)) )
| ~ big_p(a)
| big_p(f(f(X1))) ) )
& ( ? [X0] :
( ( ~ big_p(X0)
| big_p(f(X0)) )
& big_p(a)
& ~ big_p(f(f(X0))) )
| sP1 ) ),
inference(rectify,[],[f8]) ).
fof(f10,plain,
( ( ~ sP1
| ! [X1] :
( ( big_p(X1)
& ~ big_p(f(X1)) )
| ~ big_p(a)
| big_p(f(f(X1))) ) )
& ( ( ( ~ big_p(sK2)
| big_p(f(sK2)) )
& big_p(a)
& ~ big_p(f(f(sK2))) )
| sP1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f9]) ).
fof(f14,plain,
( ( sP1
| ! [X1] :
( sP0(X1)
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ) )
& ( ~ sP1
| ? [X1] :
( ~ sP0(X1)
| ( ~ big_p(f(f(X1)))
& ~ big_p(X1)
& big_p(a) ) ) ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f15,plain,
( ( sP1
| ! [X1] :
( sP0(X1)
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ) )
& ( ~ sP1
| ? [X0] :
( ~ sP0(X0)
| ( ~ big_p(f(f(X0)))
& ~ big_p(X0)
& big_p(a) ) ) ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
( ( sP1
| ! [X1] :
( sP0(X1)
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ) )
& ( ~ sP1
| ~ sP0(sK3)
| ( ~ big_p(f(f(sK3)))
& ~ big_p(sK3)
& big_p(a) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f15]) ).
fof(f17,plain,
! [X1] :
( ~ sP1
| big_p(X1)
| ~ big_p(a)
| big_p(f(f(X1))) ),
inference(cnf_transformation,[],[f10]) ).
fof(f18,plain,
! [X1] :
( ~ sP1
| ~ big_p(f(X1))
| ~ big_p(a)
| big_p(f(f(X1))) ),
inference(cnf_transformation,[],[f10]) ).
fof(f19,plain,
( ~ big_p(sK2)
| big_p(f(sK2))
| sP1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f20,plain,
( big_p(a)
| sP1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f21,plain,
( ~ big_p(f(f(sK2)))
| sP1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f26,plain,
! [X1] :
( sP1
| sP0(X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f27,plain,
! [X1] :
( sP1
| big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ),
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
( ~ sP1
| ~ sP0(sK3)
| ~ big_p(f(f(sK3))) ),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
( ~ sP1
| ~ sP0(sK3)
| ~ big_p(sK3) ),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
( ~ sP1
| ~ sP0(sK3)
| big_p(a) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_49,plain,
( sP1
| ~ big_p(f(f(sK2))) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_50,plain,
( sP1
| big_p(a) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_51,plain,
( sP1
| big_p(f(sK2))
| ~ big_p(sK2) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_52,plain,
! [X0: $i] :
( big_p(f(f(X0)))
| ~ sP1
| ~ big_p(a)
| ~ big_p(f(X0)) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_53,plain,
! [X0: $i] :
( big_p(X0)
| big_p(f(f(X0)))
| ~ sP1
| ~ big_p(a) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_58,negated_conjecture,
( big_p(a)
| ~ sP1
| ~ sP0(sK3) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_59,negated_conjecture,
( ~ sP1
| ~ sP0(sK3)
| ~ big_p(sK3) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_60,negated_conjecture,
( ~ sP1
| ~ sP0(sK3)
| ~ big_p(f(f(sK3))) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_61,negated_conjecture,
! [X0: $i] :
( sP1
| big_p(X0)
| big_p(f(f(X0)))
| ~ big_p(a) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_62,negated_conjecture,
! [X0: $i] :
( sP1
| sP0(X0) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_76,negated_conjecture,
( big_p(a)
| ~ sP0(sK3) ),
inference(global_subsumption_just,[status(thm)],[c_58,c_50,c_58]) ).
tcf(c_82,plain,
! [X0: $i] :
( big_p(X0)
| big_p(f(f(X0)))
| ~ big_p(a) ),
inference(global_subsumption_just,[status(thm)],[c_53,c_61,c_53]) ).
tcf(c_239,definition,
iPr_def_10 = f(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_240,definition,
iPr_def_11 = f(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
fof(f5,definition,
! [X1] :
( sP0(X1)
<=> ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f6,definition,
( sP1
<=> ! [X0] :
( ( big_p(X0)
& ~ big_p(f(X0)) )
| ~ big_p(a)
| big_p(f(f(X0))) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f7,plain,
( sP1
<~> ! [X1] :
( sP0(X1)
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(definition_folding,[],[f4,f6,f5]) ).
fof(f11,plain,
! [X1] :
( ( ~ sP0(X1)
| big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& ( ( ~ big_p(f(f(X1)))
& big_p(f(X1))
& big_p(a) )
| sP0(X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f12,plain,
! [X1] :
( ( ~ sP0(X1)
| big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& ( ( ~ big_p(f(f(X1)))
& big_p(f(X1))
& big_p(a) )
| sP0(X1) ) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0] :
( ( ~ sP0(X0)
| big_p(f(f(X0)))
| ~ big_p(f(X0))
| ~ big_p(a) )
& ( ( ~ big_p(f(f(X0)))
& big_p(f(X0))
& big_p(a) )
| sP0(X0) ) ),
inference(rectify,[],[f12]) ).
fof(f22,plain,
! [X0] :
( ~ sP0(X0)
| big_p(f(f(X0)))
| ~ big_p(f(X0))
| ~ big_p(a) ),
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
! [X0] :
( ~ big_p(f(f(X0)))
| sP0(X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f24,plain,
! [X0] :
( big_p(f(X0))
| sP0(X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f25,plain,
! [X0] :
( big_p(a)
| sP0(X0) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_54,plain,
! [X0: $i] :
( big_p(a)
| sP0(X0) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_55,plain,
! [X0: $i] :
( sP0(X0)
| big_p(f(X0)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_56,plain,
! [X0: $i] :
( sP0(X0)
| ~ big_p(f(f(X0))) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_57,plain,
! [X0: $i] :
( big_p(f(f(X0)))
| ~ big_p(a)
| ~ sP0(X0)
| ~ big_p(f(X0)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_69,negated_conjecture,
! [X0: $i] : sP0(X0),
inference(global_subsumption_just,[status(thm)],[c_62,c_62,c_54,c_55,c_56,c_52]) ).
tcf(c_78,plain,
! [X0: $i] : sP0(X0),
inference(global_subsumption_just,[status(thm)],[c_56,c_62,c_54,c_55,c_56,c_52]) ).
tcf(c_84,plain,
! [X0: $i] :
( big_p(f(f(X0)))
| ~ big_p(f(X0))
| ~ big_p(a) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_57,c_69]) ).
tcf(c_85,plain,
! [X0: $i] :
( big_p(f(f(X0)))
| ~ big_p(a)
| ~ big_p(f(X0)) ),
inference(renaming,[status(thm)],[c_84]) ).
tcf(c_87,plain,
! [X0: $i] :
( big_p(f(f(X0)))
| ~ big_p(a)
| ~ big_p(f(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_57,c_85]) ).
tcf(c_91,plain,
big_p(a),
inference(backward_subsumption_resolution,[status(thm)],[c_76,c_78]) ).
tcf(c_92,plain,
( ~ sP1
| ~ big_p(sK3) ),
inference(backward_subsumption_resolution,[status(thm)],[c_59,c_78]) ).
tcf(c_93,plain,
( ~ sP1
| ~ big_p(f(f(sK3))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_60,c_78]) ).
tcf(c_96,plain,
! [X0: $i] :
( big_p(X0)
| big_p(f(f(X0))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_82,c_91]) ).
tcf(c_97,plain,
! [X0: $i] :
( big_p(f(f(X0)))
| ~ big_p(f(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_87,c_91]) ).
tcf(c_241,plain,
! [X0: $i] :
( big_p(f(f(X0)))
| ~ big_p(f(X0)) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_242,plain,
! [X0: $i] :
( big_p(X0)
| big_p(f(f(X0))) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_243,plain,
( ~ sP1
| ~ big_p(iPr_def_11) ),
inference(demodulation,[status(thm)],[c_93,c_239,c_240]) ).
tcf(c_244,plain,
( ~ sP1
| ~ big_p(sK3) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_366,plain,
( big_p(sK3)
| big_p(f(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_239,c_242]) ).
tcf(c_367,plain,
( big_p(iPr_def_11)
| big_p(sK3) ),
inference(light_normalisation,[status(thm)],[c_366,c_240]) ).
tcf(c_377,plain,
( big_p(iPr_def_11)
| ~ sP1 ),
inference(superposition,[status(thm)],[c_367,c_244]) ).
tcf(c_380,plain,
~ sP1,
inference(global_subsumption_just,[status(thm)],[c_377,c_243,c_377]) ).
tcf(c_393,plain,
~ big_p(f(f(sK2))),
inference(global_subsumption_just,[status(thm)],[c_49,c_49,c_380]) ).
tcf(c_395,plain,
~ big_p(f(sK2)),
inference(superposition,[status(thm)],[c_241,c_393]) ).
tcf(c_396,plain,
big_p(sK2),
inference(superposition,[status(thm)],[c_242,c_393]) ).
tcf(c_397,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_395,c_396,c_380,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN084+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.37 % Computer : n005.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Fri Sep 25 00:07:50 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 1.65/1.27 % SZS status Started for theBenchmark.p
% 1.65/1.27 % SZS status Theorem for theBenchmark.p
% 1.65/1.27
% 1.65/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.65/1.27
% 1.65/1.27 % ------ iProver source info
% 1.65/1.27
% 1.65/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.65/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.65/1.27 % git: non_committed_changes: false
% 1.65/1.27
% 1.65/1.27 % ------ Parsing...
% 1.65/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.65/1.27
% 1.65/1.27 % ------ Preprocessing... sf_s rm: 2 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.65/1.27
% 1.65/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.65/1.27
% 1.65/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.65/1.27 % ------ Proving...
% 1.65/1.27 % ------ Problem Properties
% 1.65/1.27
% 1.65/1.27 %
% 1.65/1.27 % clauses 8
% 1.65/1.27 % conjectures 0
% 1.65/1.27 % EPR 2
% 1.65/1.27 % Horn 6
% 1.65/1.27 % unary 2
% 1.65/1.27 % binary 5
% 1.65/1.27 % lits 15
% 1.65/1.27 % lits eq 2
% 1.65/1.27 % fd_pure 0
% 1.65/1.27 % fd_pseudo 0
% 1.65/1.27 % fd_cond 0
% 1.65/1.27 % fd_pseudo_cond 0
% 1.65/1.27 % AC symbols 0
% 1.65/1.27
% 1.65/1.27 % ------ Schedule dynamic 5 is on
% 1.65/1.27
% 1.65/1.27 % ------ no conjectures: strip conj schedule
% 1.65/1.27
% 1.65/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.65/1.27
% 1.65/1.27
% 1.65/1.27 % ------
% 1.65/1.27 % Current options:
% 1.65/1.27 % ------
% 1.65/1.27
% 1.65/1.27
% 1.65/1.27 %
% 1.65/1.27
% 1.65/1.27 % ------ Proving...
% 1.65/1.27 %
% 1.65/1.27
% 1.65/1.27 % SZS status Theorem for theBenchmark.p
% 1.65/1.27
% 1.65/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.65/1.27
% 1.65/1.27
%------------------------------------------------------------------------------