TSTP Solution File: SYN084+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SYN084+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 03:05:13 EDT 2023
% Result : Theorem 1.50s 1.13s
% Output : CNFRefutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 66 ( 4 unt; 0 def)
% Number of atoms : 276 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 341 ( 131 ~; 146 |; 51 &)
% ( 4 <=>; 6 =>; 0 <=; 3 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 2 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 50 ( 4 sgn; 28 !; 6 ?)
% 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/sandbox/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,[],[f1]) ).
fof(f3,plain,
( ! [X0] :
( big_p(f(f(X0)))
| ( ~ big_p(f(X0))
& big_p(X0) )
| ~ big_p(a) )
<~> ! [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(f(f(X0)))
| ( ~ big_p(f(X0))
& big_p(X0) )
| ~ big_p(a) )
<~> ! [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(f5,plain,
! [X1] :
( sP0(X1)
<=> ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f6,plain,
( sP1
<=> ! [X0] :
( big_p(f(f(X0)))
| ( ~ big_p(f(X0))
& big_p(X0) )
| ~ big_p(a) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f7,plain,
( sP1
<~> ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& sP0(X1) ) ),
inference(definition_folding,[],[f4,f6,f5]) ).
fof(f8,plain,
( ( sP1
| ? [X0] :
( ~ big_p(f(f(X0)))
& ( big_p(f(X0))
| ~ big_p(X0) )
& big_p(a) ) )
& ( ! [X0] :
( big_p(f(f(X0)))
| ( ~ big_p(f(X0))
& big_p(X0) )
| ~ big_p(a) )
| ~ sP1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f9,plain,
( ( sP1
| ? [X0] :
( ~ big_p(f(f(X0)))
& ( big_p(f(X0))
| ~ big_p(X0) )
& big_p(a) ) )
& ( ! [X1] :
( big_p(f(f(X1)))
| ( ~ big_p(f(X1))
& big_p(X1) )
| ~ big_p(a) )
| ~ sP1 ) ),
inference(rectify,[],[f8]) ).
fof(f10,plain,
( ? [X0] :
( ~ big_p(f(f(X0)))
& ( big_p(f(X0))
| ~ big_p(X0) )
& big_p(a) )
=> ( ~ big_p(f(f(sK2)))
& ( big_p(f(sK2))
| ~ big_p(sK2) )
& big_p(a) ) ),
introduced(choice_axiom,[]) ).
fof(f11,plain,
( ( sP1
| ( ~ big_p(f(f(sK2)))
& ( big_p(f(sK2))
| ~ big_p(sK2) )
& big_p(a) ) )
& ( ! [X1] :
( big_p(f(f(X1)))
| ( ~ big_p(f(X1))
& big_p(X1) )
| ~ big_p(a) )
| ~ sP1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f9,f10]) ).
fof(f12,plain,
! [X1] :
( ( sP0(X1)
| ( ~ big_p(f(f(X1)))
& ~ big_p(X1)
& big_p(a) ) )
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a)
| ~ sP0(X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f13,plain,
! [X1] :
( ( sP0(X1)
| ( ~ big_p(f(f(X1)))
& ~ big_p(X1)
& big_p(a) ) )
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a)
| ~ sP0(X1) ) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
! [X0] :
( ( sP0(X0)
| ( ~ big_p(f(f(X0)))
& ~ big_p(X0)
& big_p(a) ) )
& ( big_p(f(f(X0)))
| big_p(X0)
| ~ big_p(a)
| ~ sP0(X0) ) ),
inference(rectify,[],[f13]) ).
fof(f15,plain,
( ( ? [X1] :
( ( ~ big_p(f(f(X1)))
& big_p(f(X1))
& big_p(a) )
| ~ sP0(X1) )
| ~ sP1 )
& ( ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& sP0(X1) )
| sP1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f16,plain,
( ( ? [X0] :
( ( ~ big_p(f(f(X0)))
& big_p(f(X0))
& big_p(a) )
| ~ sP0(X0) )
| ~ sP1 )
& ( ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& sP0(X1) )
| sP1 ) ),
inference(rectify,[],[f15]) ).
fof(f17,plain,
( ? [X0] :
( ( ~ big_p(f(f(X0)))
& big_p(f(X0))
& big_p(a) )
| ~ sP0(X0) )
=> ( ( ~ big_p(f(f(sK3)))
& big_p(f(sK3))
& big_p(a) )
| ~ sP0(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
( ( ( ~ big_p(f(f(sK3)))
& big_p(f(sK3))
& big_p(a) )
| ~ sP0(sK3)
| ~ sP1 )
& ( ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& sP0(X1) )
| sP1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f16,f17]) ).
fof(f19,plain,
! [X1] :
( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a)
| ~ sP1 ),
inference(cnf_transformation,[],[f11]) ).
fof(f20,plain,
! [X1] :
( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a)
| ~ sP1 ),
inference(cnf_transformation,[],[f11]) ).
fof(f21,plain,
( sP1
| big_p(a) ),
inference(cnf_transformation,[],[f11]) ).
fof(f22,plain,
( sP1
| big_p(f(sK2))
| ~ big_p(sK2) ),
inference(cnf_transformation,[],[f11]) ).
fof(f23,plain,
( sP1
| ~ big_p(f(f(sK2))) ),
inference(cnf_transformation,[],[f11]) ).
fof(f24,plain,
! [X0] :
( big_p(f(f(X0)))
| big_p(X0)
| ~ big_p(a)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X0] :
( sP0(X0)
| big_p(a) ),
inference(cnf_transformation,[],[f14]) ).
fof(f26,plain,
! [X0] :
( sP0(X0)
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X0] :
( sP0(X0)
| ~ big_p(f(f(X0))) ),
inference(cnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X1] :
( sP0(X1)
| sP1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X1] :
( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a)
| sP1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
( big_p(a)
| ~ sP0(sK3)
| ~ sP1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
( big_p(f(sK3))
| ~ sP0(sK3)
| ~ sP1 ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
( ~ big_p(f(f(sK3)))
| ~ sP0(sK3)
| ~ sP1 ),
inference(cnf_transformation,[],[f18]) ).
cnf(c_49,plain,
( ~ big_p(f(f(sK2)))
| sP1 ),
inference(cnf_transformation,[],[f23]) ).
cnf(c_50,plain,
( ~ big_p(sK2)
| big_p(f(sK2))
| sP1 ),
inference(cnf_transformation,[],[f22]) ).
cnf(c_51,plain,
( big_p(a)
| sP1 ),
inference(cnf_transformation,[],[f21]) ).
cnf(c_52,plain,
( ~ big_p(f(X0))
| ~ big_p(a)
| ~ sP1
| big_p(f(f(X0))) ),
inference(cnf_transformation,[],[f20]) ).
cnf(c_53,plain,
( ~ big_p(a)
| ~ sP1
| big_p(f(f(X0)))
| big_p(X0) ),
inference(cnf_transformation,[],[f19]) ).
cnf(c_54,plain,
( ~ big_p(f(f(X0)))
| sP0(X0) ),
inference(cnf_transformation,[],[f27]) ).
cnf(c_55,plain,
( ~ big_p(X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f26]) ).
cnf(c_56,plain,
( sP0(X0)
| big_p(a) ),
inference(cnf_transformation,[],[f25]) ).
cnf(c_57,plain,
( ~ sP0(X0)
| ~ big_p(a)
| big_p(f(f(X0)))
| big_p(X0) ),
inference(cnf_transformation,[],[f24]) ).
cnf(c_58,negated_conjecture,
( ~ big_p(f(f(sK3)))
| ~ sP0(sK3)
| ~ sP1 ),
inference(cnf_transformation,[],[f32]) ).
cnf(c_59,negated_conjecture,
( ~ sP0(sK3)
| ~ sP1
| big_p(f(sK3)) ),
inference(cnf_transformation,[],[f31]) ).
cnf(c_60,negated_conjecture,
( ~ sP0(sK3)
| ~ sP1
| big_p(a) ),
inference(cnf_transformation,[],[f30]) ).
cnf(c_61,negated_conjecture,
( ~ big_p(f(X0))
| ~ big_p(a)
| big_p(f(f(X0)))
| sP1 ),
inference(cnf_transformation,[],[f29]) ).
cnf(c_62,negated_conjecture,
( sP0(X0)
| sP1 ),
inference(cnf_transformation,[],[f28]) ).
cnf(c_69,negated_conjecture,
sP0(X0),
inference(global_subsumption_just,[status(thm)],[c_62,c_62,c_56,c_55,c_54,c_53]) ).
cnf(c_76,negated_conjecture,
( ~ sP0(sK3)
| big_p(a) ),
inference(global_subsumption_just,[status(thm)],[c_60,c_51,c_60]) ).
cnf(c_78,plain,
sP0(X0),
inference(global_subsumption_just,[status(thm)],[c_54,c_69]) ).
cnf(c_82,negated_conjecture,
( ~ big_p(f(X0))
| big_p(f(f(X0)))
| sP1 ),
inference(global_subsumption_just,[status(thm)],[c_61,c_51,c_61]) ).
cnf(c_85,plain,
( ~ big_p(a)
| big_p(f(f(X0)))
| big_p(X0) ),
inference(global_subsumption_just,[status(thm)],[c_57,c_62,c_56,c_55,c_54,c_53,c_57]) ).
cnf(c_87,plain,
( ~ big_p(a)
| ~ big_p(f(X0))
| big_p(f(f(X0))) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_52,c_82]) ).
cnf(c_88,plain,
( ~ big_p(f(X0))
| ~ big_p(a)
| big_p(f(f(X0))) ),
inference(renaming,[status(thm)],[c_87]) ).
cnf(c_92,plain,
big_p(a),
inference(backward_subsumption_resolution,[status(thm)],[c_76,c_78]) ).
cnf(c_93,plain,
( ~ sP1
| big_p(f(sK3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_59,c_78]) ).
cnf(c_94,plain,
( ~ big_p(f(f(sK3)))
| ~ sP1 ),
inference(backward_subsumption_resolution,[status(thm)],[c_58,c_78]) ).
cnf(c_97,plain,
( big_p(f(f(X0)))
| big_p(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_85,c_92]) ).
cnf(c_98,plain,
( ~ big_p(f(X0))
| big_p(f(f(X0))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_88,c_92]) ).
cnf(c_126,plain,
( ~ big_p(f(f(sK3)))
| ~ big_p(sK2)
| big_p(f(sK2)) ),
inference(resolution,[status(thm)],[c_50,c_94]) ).
cnf(c_136,plain,
( ~ big_p(sK2)
| big_p(f(sK2))
| big_p(f(sK3)) ),
inference(resolution,[status(thm)],[c_50,c_93]) ).
cnf(c_146,plain,
( ~ big_p(f(f(sK2)))
| ~ big_p(f(f(sK3))) ),
inference(resolution,[status(thm)],[c_49,c_94]) ).
cnf(c_153,plain,
( ~ big_p(f(f(sK2)))
| big_p(f(sK3)) ),
inference(resolution,[status(thm)],[c_49,c_93]) ).
cnf(c_243,plain,
( ~ big_p(f(sK3))
| big_p(f(f(sK3))) ),
inference(instantiation,[status(thm)],[c_98]) ).
cnf(c_246,plain,
( big_p(f(f(sK2)))
| big_p(sK2) ),
inference(instantiation,[status(thm)],[c_97]) ).
cnf(c_247,plain,
( ~ big_p(f(sK2))
| big_p(f(f(sK2))) ),
inference(instantiation,[status(thm)],[c_98]) ).
cnf(c_252,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_247,c_246,c_243,c_153,c_146,c_136,c_126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYN084+1 : TPTP v8.1.2. Released v2.0.0.
% 0.11/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 17:03:50 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.45 Running first-order theorem proving
% 0.18/0.45 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 1.50/1.13 % SZS status Started for theBenchmark.p
% 1.50/1.13 % SZS status Theorem for theBenchmark.p
% 1.50/1.13
% 1.50/1.13 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.50/1.13
% 1.50/1.13 ------ iProver source info
% 1.50/1.13
% 1.50/1.13 git: date: 2023-05-31 18:12:56 +0000
% 1.50/1.13 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.50/1.13 git: non_committed_changes: false
% 1.50/1.13 git: last_make_outside_of_git: false
% 1.50/1.13
% 1.50/1.13 ------ Parsing...
% 1.50/1.13 ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.50/1.13
% 1.50/1.13 ------ Preprocessing... sf_s rm: 2 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e
% 1.50/1.13
% 1.50/1.13 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.50/1.13 ------ Proving...
% 1.50/1.13 ------ Problem Properties
% 1.50/1.13
% 1.50/1.13
% 1.50/1.13 clauses 6
% 1.50/1.13 conjectures 0
% 1.50/1.13 EPR 0
% 1.50/1.13 Horn 4
% 1.50/1.13 unary 0
% 1.50/1.13 binary 5
% 1.50/1.13 lits 13
% 1.50/1.13 lits eq 0
% 1.50/1.13 fd_pure 0
% 1.50/1.13 fd_pseudo 0
% 1.50/1.13 fd_cond 0
% 1.50/1.13 fd_pseudo_cond 0
% 1.50/1.13 AC symbols 0
% 1.50/1.13
% 1.50/1.13 ------ Schedule dynamic 5 is on
% 1.50/1.13
% 1.50/1.13 ------ no conjectures: strip conj schedule
% 1.50/1.13
% 1.50/1.13 ------ no equalities: superposition off
% 1.50/1.13
% 1.50/1.13 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.50/1.13
% 1.50/1.13
% 1.50/1.13 ------
% 1.50/1.13 Current options:
% 1.50/1.13 ------
% 1.50/1.13
% 1.50/1.13
% 1.50/1.13
% 1.50/1.13
% 1.50/1.13 ------ Proving...
% 1.50/1.13
% 1.50/1.13
% 1.50/1.13 % SZS status Theorem for theBenchmark.p
% 1.50/1.13
% 1.50/1.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.50/1.13
% 1.50/1.14
%------------------------------------------------------------------------------