TSTP Solution File: ITP328_1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n029.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 May 3 02:30:40 EDT 2024
% Result : Theorem 11.80s 2.14s
% Output : CNFRefutation 11.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 333 ( 26 equ)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 64 ( 31 ~; 18 |; 6 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 256 ( 256 fml; 0 var)
% Number arithmetic : 59 ( 13 atm; 31 fun; 4 num; 11 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 12 usr; 8 prp; 0-2 aty)
% Number of functors : 6 ( 0 usr; 1 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 37 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
tff(f6,conjecture,
( ( ~ $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))
=> ( 'fun_app$e'('of_nat$','to_nat$'('x$')) = $sum('fun_app$e'('of_nat$','to_nat$'('i$')),$difference('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))) ) )
& ( $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))
=> ( 'fun_app$e'('of_nat$','to_nat$'('x$')) = $sum('fun_app$e'('of_nat$','to_nat$'('i$')),0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture5) ).
tff(f7,negated_conjecture,
~ ( ( ~ $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))
=> ( 'fun_app$e'('of_nat$','to_nat$'('x$')) = $sum('fun_app$e'('of_nat$','to_nat$'('i$')),$difference('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))) ) )
& ( $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))
=> ( 'fun_app$e'('of_nat$','to_nat$'('x$')) = $sum('fun_app$e'('of_nat$','to_nat$'('i$')),0) ) ) ),
inference(negated_conjecture,[],[f6]) ).
tff(f15,axiom,
! [X0: $int,X1: $int] : ( $difference($sum(X0,X1),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom13) ).
tff(f18,axiom,
'fun_app$d'('fun_app$g'('less_eq$','i$'),'x$'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom16) ).
tff(f26,axiom,
! [X0: 'N$',X1: 'N$'] :
( 'fun_app$d'('fun_app$g'('less_eq$',X0),X1)
=> $lesseq('fun_app$e'('of_nat$','to_nat$'(X0)),'fun_app$e'('of_nat$','to_nat$'(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom24) ).
tff(f55,axiom,
! [X0: 'Int_set_set$',X1: 'Int_set_set$'] : ( 'plus$a'(X0,X1) = 'plus$a'(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom53) ).
tff(f63,axiom,
! [X0: 'Int_set_set$',X1: 'Int_set_set$',X2: 'Int_set_set$'] : ( 'plus$a'(X0,'plus$a'(X1,X2)) = 'plus$a'('plus$a'(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom61) ).
tff(f572,axiom,
! [X0: 'N$',X1: 'N$'] :
( ~ 'fun_app$d'('fun_app$g'('less_eq$',X0),X1)
<=> 'fun_app$d'('fun_app$g'('less$',X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom570) ).
tff(f623,plain,
~ ( ( ~ $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))
=> ( 'fun_app$e'('of_nat$','to_nat$'('x$')) = $sum('fun_app$e'('of_nat$','to_nat$'('i$')),$sum('fun_app$e'('of_nat$','to_nat$'('x$')),$uminus('fun_app$e'('of_nat$','to_nat$'('i$'))))) ) )
& ( $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))
=> ( 'fun_app$e'('of_nat$','to_nat$'('x$')) = $sum('fun_app$e'('of_nat$','to_nat$'('i$')),0) ) ) ),
inference(theory_normalization,[],[f7]) ).
tff(f629,plain,
! [X0: $int,X1: $int] : ( $sum($sum(X0,X1),$uminus(X0)) = X1 ),
inference(theory_normalization,[],[f15]) ).
tff(f634,plain,
! [X0: 'N$',X1: 'N$'] :
( 'fun_app$d'('fun_app$g'('less_eq$',X0),X1)
=> ~ $less('fun_app$e'('of_nat$','to_nat$'(X1)),'fun_app$e'('of_nat$','to_nat$'(X0))) ),
inference(theory_normalization,[],[f26]) ).
tff(f864,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_138,[]) ).
tff(f865,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_139,[]) ).
tff(f982,plain,
( ( ( 'fun_app$e'('of_nat$','to_nat$'('x$')) != $sum('fun_app$e'('of_nat$','to_nat$'('i$')),$sum('fun_app$e'('of_nat$','to_nat$'('x$')),$uminus('fun_app$e'('of_nat$','to_nat$'('i$'))))) )
& ~ $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$'))) )
| ( ( 'fun_app$e'('of_nat$','to_nat$'('x$')) != $sum('fun_app$e'('of_nat$','to_nat$'('i$')),0) )
& $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$'))) ) ),
inference(ennf_transformation,[],[f623]) ).
tff(f986,plain,
! [X0: 'N$',X1: 'N$'] :
( ~ $less('fun_app$e'('of_nat$','to_nat$'(X1)),'fun_app$e'('of_nat$','to_nat$'(X0)))
| ~ 'fun_app$d'('fun_app$g'('less_eq$',X0),X1) ),
inference(ennf_transformation,[],[f634]) ).
tff(f2142,plain,
! [X0: 'N$',X1: 'N$'] :
( ( ~ 'fun_app$d'('fun_app$g'('less_eq$',X0),X1)
| ~ 'fun_app$d'('fun_app$g'('less$',X1),X0) )
& ( 'fun_app$d'('fun_app$g'('less$',X1),X0)
| 'fun_app$d'('fun_app$g'('less_eq$',X0),X1) ) ),
inference(nnf_transformation,[],[f572]) ).
tff(f2176,plain,
( ( 'fun_app$e'('of_nat$','to_nat$'('x$')) != $sum('fun_app$e'('of_nat$','to_nat$'('i$')),$sum('fun_app$e'('of_nat$','to_nat$'('x$')),$uminus('fun_app$e'('of_nat$','to_nat$'('i$'))))) )
| $less('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$'))) ),
inference(cnf_transformation,[],[f982]) ).
tff(f2201,plain,
! [X0: $int,X1: $int] : ( $sum($sum(X0,X1),$uminus(X0)) = X1 ),
inference(cnf_transformation,[],[f629]) ).
tff(f2204,plain,
'fun_app$d'('fun_app$g'('less_eq$','i$'),'x$'),
inference(cnf_transformation,[],[f18]) ).
tff(f2219,plain,
! [X0: 'N$',X1: 'N$'] :
( ~ $less('fun_app$e'('of_nat$','to_nat$'(X1)),'fun_app$e'('of_nat$','to_nat$'(X0)))
| ~ 'fun_app$d'('fun_app$g'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f986]) ).
tff(f2255,plain,
! [X0: 'Int_set_set$',X1: 'Int_set_set$'] : ( 'plus$a'(X0,X1) = 'plus$a'(X1,X0) ),
inference(cnf_transformation,[],[f55]) ).
tff(f2267,plain,
! [X2: 'Int_set_set$',X0: 'Int_set_set$',X1: 'Int_set_set$'] : ( 'plus$a'(X0,'plus$a'(X1,X2)) = 'plus$a'('plus$a'(X0,X1),X2) ),
inference(cnf_transformation,[],[f63]) ).
tff(f3399,plain,
! [X0: 'N$',X1: 'N$'] :
( 'fun_app$d'('fun_app$g'('less$',X1),X0)
| 'fun_app$d'('fun_app$g'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f2142]) ).
tff(f3400,plain,
! [X0: 'N$',X1: 'N$'] :
( ~ 'fun_app$d'('fun_app$g'('less_eq$',X0),X1)
| ~ 'fun_app$d'('fun_app$g'('less$',X1),X0) ),
inference(cnf_transformation,[],[f2142]) ).
cnf(c_59,plain,
$sum_int($sum_int(X0_3,X1_3),X2_3) = $sum_int(X0_3,$sum_int(X1_3,X2_3)),
inference(cnf_transformation,[],[f865]) ).
cnf(c_60,plain,
$sum_int(X0_3,X1_3) = $sum_int(X1_3,X0_3),
inference(cnf_transformation,[],[f864]) ).
cnf(c_71,negated_conjecture,
( $sum_int('fun_app$e'('of_nat$','to_nat$'('i$')),$sum_int('fun_app$e'('of_nat$','to_nat$'('x$')),$uminus_int('fun_app$e'('of_nat$','to_nat$'('i$'))))) != 'fun_app$e'('of_nat$','to_nat$'('x$'))
| $less_int('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$'))) ),
inference(cnf_transformation,[],[f2176]) ).
cnf(c_87,plain,
$sum_int($sum_int(X0_3,X1_3),$uminus_int(X0_3)) = X1_3,
inference(cnf_transformation,[],[f2201]) ).
cnf(c_90,plain,
'fun_app$d'('fun_app$g'('less_eq$','i$'),'x$'),
inference(cnf_transformation,[],[f2204]) ).
cnf(c_100,plain,
( ~ $less_int('fun_app$e'('of_nat$','to_nat$'(X0_26)),'fun_app$e'('of_nat$','to_nat$'(X1_26)))
| ~ 'fun_app$d'('fun_app$g'('less_eq$',X1_26),X0_26) ),
inference(cnf_transformation,[],[f2219]) ).
cnf(c_136,plain,
'plus$a'(X0_18,X1_18) = 'plus$a'(X1_18,X0_18),
inference(cnf_transformation,[],[f2255]) ).
cnf(c_144,plain,
'plus$a'('plus$a'(X0_18,X1_18),X2_18) = 'plus$a'(X0_18,'plus$a'(X1_18,X2_18)),
inference(cnf_transformation,[],[f2267]) ).
cnf(c_1131,plain,
( ~ 'fun_app$d'('fun_app$g'('less$',X0_26),X1_26)
| ~ 'fun_app$d'('fun_app$g'('less_eq$',X1_26),X0_26) ),
inference(cnf_transformation,[],[f3400]) ).
cnf(c_1132,plain,
( 'fun_app$d'('fun_app$g'('less$',X0_26),X1_26)
| 'fun_app$d'('fun_app$g'('less_eq$',X1_26),X0_26) ),
inference(cnf_transformation,[],[f3399]) ).
cnf(c_1822,plain,
$sum_int(X0_3,$sum_int(X1_3,$uminus_int(X0_3))) = X1_3,
inference(theory_normalisation,[status(thm)],[c_87,c_144,c_136,c_59,c_60]) ).
cnf(c_1997,plain,
( 'fun_app$d'('fun_app$g'('less$',X0_26),X1_26)
| ~ $less_int('fun_app$e'('of_nat$','to_nat$'(X0_26)),'fun_app$e'('of_nat$','to_nat$'(X1_26))) ),
inference(prop_impl_just,[status(thm)],[c_1132,c_100]) ).
cnf(c_1998,plain,
( ~ $less_int('fun_app$e'('of_nat$','to_nat$'(X0_26)),'fun_app$e'('of_nat$','to_nat$'(X1_26)))
| 'fun_app$d'('fun_app$g'('less$',X0_26),X1_26) ),
inference(renaming,[status(thm)],[c_1997]) ).
cnf(c_2063,plain,
( $sum_int('fun_app$e'('of_nat$','to_nat$'('i$')),$sum_int('fun_app$e'('of_nat$','to_nat$'('x$')),$uminus_int('fun_app$e'('of_nat$','to_nat$'('i$'))))) != 'fun_app$e'('of_nat$','to_nat$'('x$'))
| $less_int('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$'))) ),
inference(prop_impl_just,[status(thm)],[c_71]) ).
cnf(c_3616,plain,
$less_int('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$'))),
inference(backward_subsumption_resolution,[status(thm)],[c_2063,c_1822]) ).
cnf(c_16185,plain,
( 'fun_app$d'('fun_app$g'('less$',X0_26),X1_26)
| ~ $less_int('fun_app$e'('of_nat$','to_nat$'(X0_26)),'fun_app$e'('of_nat$','to_nat$'(X1_26))) ),
inference(prop_impl_just,[status(thm)],[c_1998]) ).
cnf(c_16186,plain,
( ~ $less_int('fun_app$e'('of_nat$','to_nat$'(X0_26)),'fun_app$e'('of_nat$','to_nat$'(X1_26)))
| 'fun_app$d'('fun_app$g'('less$',X0_26),X1_26) ),
inference(renaming,[status(thm)],[c_16185]) ).
cnf(c_32390,plain,
( ~ $less_int('fun_app$e'('of_nat$','to_nat$'('x$')),'fun_app$e'('of_nat$','to_nat$'('i$')))
| 'fun_app$d'('fun_app$g'('less$','x$'),'i$') ),
inference(instantiation,[status(thm)],[c_16186]) ).
cnf(c_32765,plain,
~ 'fun_app$d'('fun_app$g'('less$','x$'),'i$'),
inference(superposition,[status(thm)],[c_90,c_1131]) ).
cnf(c_32770,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_32765,c_32390,c_3616]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.11/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu May 2 22:07:52 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running TFA theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --no_cores 8 --schedule casc_29_tfa --heuristic_context casc_unsat /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 11.80/2.14 % SZS status Started for theBenchmark.p
% 11.80/2.14 % SZS status Theorem for theBenchmark.p
% 11.80/2.14
% 11.80/2.14 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 11.80/2.14
% 11.80/2.14 ------ iProver source info
% 11.80/2.14
% 11.80/2.14 git: date: 2024-05-02 19:28:25 +0000
% 11.80/2.14 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 11.80/2.14 git: non_committed_changes: false
% 11.80/2.14
% 11.80/2.14 ------ Parsing...
% 11.80/2.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 11.80/2.14
% 11.80/2.14 ------ Preprocessing... sup_sim: 80 sf_s rm: 20 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e
% 11.80/2.14
% 11.80/2.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 11.80/2.14
% 11.80/2.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 11.80/2.14 ------ Proving...
% 11.80/2.14 ------ Problem Properties
% 11.80/2.14
% 11.80/2.14
% 11.80/2.14 clauses 443
% 11.80/2.14 conjectures 0
% 11.80/2.14 EPR 8
% 11.80/2.14 Horn 239
% 11.80/2.14 unary 56
% 11.80/2.14 binary 102
% 11.80/2.14 lits 1253
% 11.80/2.14 lits eq 124
% 11.80/2.14 fd_pure 1
% 11.80/2.14 fd_pseudo 0
% 11.80/2.14 fd_cond 0
% 11.80/2.14 fd_pseudo_cond 12
% 11.80/2.14 AC symbols 2
% 11.80/2.14
% 11.80/2.14 ------ Input Options Time Limit: Unbounded
% 11.80/2.14
% 11.80/2.14
% 11.80/2.14 ------
% 11.80/2.14 Current options:
% 11.80/2.14 ------
% 11.80/2.14
% 11.80/2.14
% 11.80/2.14
% 11.80/2.14
% 11.80/2.14 ------ Proving...
% 11.80/2.14
% 11.80/2.14
% 11.80/2.14 % SZS status Theorem for theBenchmark.p
% 11.80/2.14
% 11.80/2.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 11.80/2.14
% 11.80/2.15
%------------------------------------------------------------------------------