TSTP Solution File: ARI616_1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : ARI616_1 : TPTP v8.1.2. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n022.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 02:07:23 EDT 2024
% Result : Theorem 3.20s 1.12s
% Output : CNFRefutation 3.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 143 ( 6 equ)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 122 ( 45 ~; 24 |; 38 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 38 ( 38 fml; 0 var)
% Number arithmetic : 198 ( 40 atm; 78 fun; 0 num; 80 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 6 usr; 6 prp; 0-3 aty)
% Number of functors : 4 ( 0 usr; 0 con; 1-2 aty)
% Number of variables : 98 ( 0 sgn 49 !; 31 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
tff(f1,conjecture,
( ! [X0: $int,X1: $int,X2: $int] :
( ( $lesseq(X0,$sum(X1,X2))
& $lesseq($sum(X1,$uminus(X2)),X0) )
<=> p(X0,X1,X2) )
=> ! [X3: $int,X4: $int,X5: $int,X6: $int] :
( ? [X0: $int] :
( p(X0,X5,X6)
& p(X0,X3,X4) )
=> $lesseq($sum(X3,$uminus(X5)),$sum(X4,X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_of_radii_gt_distance_of_centers) ).
tff(f2,negated_conjecture,
~ ( ! [X0: $int,X1: $int,X2: $int] :
( ( $lesseq(X0,$sum(X1,X2))
& $lesseq($sum(X1,$uminus(X2)),X0) )
<=> p(X0,X1,X2) )
=> ! [X3: $int,X4: $int,X5: $int,X6: $int] :
( ? [X0: $int] :
( p(X0,X5,X6)
& p(X0,X3,X4) )
=> $lesseq($sum(X3,$uminus(X5)),$sum(X4,X6)) ) ),
inference(negated_conjecture,[],[f1]) ).
tff(f3,plain,
~ ( ! [X0: $int,X1: $int,X2: $int] :
( ( ~ $less($sum(X1,X2),X0)
& ~ $less(X0,$sum(X1,$uminus(X2))) )
<=> p(X0,X1,X2) )
=> ! [X3: $int,X4: $int,X5: $int,X6: $int] :
( ? [X0: $int] :
( p(X0,X5,X6)
& p(X0,X3,X4) )
=> ~ $less($sum(X4,X6),$sum(X3,$uminus(X5))) ) ),
inference(theory_normalization,[],[f2]) ).
tff(f16,plain,
~ ( ! [X0: $int,X1: $int,X2: $int] :
( ( ~ $less($sum(X1,X2),X0)
& ~ $less(X0,$sum(X1,$uminus(X2))) )
<=> p(X0,X1,X2) )
=> ! [X3: $int,X4: $int,X5: $int,X6: $int] :
( ? [X7: $int] :
( p(X7,X5,X6)
& p(X7,X3,X4) )
=> ~ $less($sum(X4,X6),$sum(X3,$uminus(X5))) ) ),
inference(rectify,[],[f3]) ).
tff(f17,plain,
( ? [X3: $int,X4: $int,X5: $int,X6: $int] :
( $less($sum(X4,X6),$sum(X3,$uminus(X5)))
& ? [X7: $int] :
( p(X7,X5,X6)
& p(X7,X3,X4) ) )
& ! [X0: $int,X1: $int,X2: $int] :
( ( ~ $less($sum(X1,X2),X0)
& ~ $less(X0,$sum(X1,$uminus(X2))) )
<=> p(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f16]) ).
tff(f18,plain,
( ? [X3: $int,X4: $int,X5: $int,X6: $int] :
( $less($sum(X4,X6),$sum(X3,$uminus(X5)))
& ? [X7: $int] :
( p(X7,X5,X6)
& p(X7,X3,X4) ) )
& ! [X0: $int,X1: $int,X2: $int] :
( ( ( ~ $less($sum(X1,X2),X0)
& ~ $less(X0,$sum(X1,$uminus(X2))) )
| ~ p(X0,X1,X2) )
& ( p(X0,X1,X2)
| $less($sum(X1,X2),X0)
| $less(X0,$sum(X1,$uminus(X2))) ) ) ),
inference(nnf_transformation,[],[f17]) ).
tff(f19,plain,
( ? [X3: $int,X4: $int,X5: $int,X6: $int] :
( $less($sum(X4,X6),$sum(X3,$uminus(X5)))
& ? [X7: $int] :
( p(X7,X5,X6)
& p(X7,X3,X4) ) )
& ! [X0: $int,X1: $int,X2: $int] :
( ( ( ~ $less($sum(X1,X2),X0)
& ~ $less(X0,$sum(X1,$uminus(X2))) )
| ~ p(X0,X1,X2) )
& ( p(X0,X1,X2)
| $less($sum(X1,X2),X0)
| $less(X0,$sum(X1,$uminus(X2))) ) ) ),
inference(flattening,[],[f18]) ).
tff(f20,plain,
( ? [X0: $int,X1: $int,X2: $int,X3: $int] :
( $less($sum(X1,X3),$sum(X0,$uminus(X2)))
& ? [X4: $int] :
( p(X4,X2,X3)
& p(X4,X0,X1) ) )
& ! [X5: $int,X6: $int,X7: $int] :
( ( ( ~ $less($sum(X6,X7),X5)
& ~ $less(X5,$sum(X6,$uminus(X7))) )
| ~ p(X5,X6,X7) )
& ( p(X5,X6,X7)
| $less($sum(X6,X7),X5)
| $less(X5,$sum(X6,$uminus(X7))) ) ) ),
inference(rectify,[],[f19]) ).
tff(f21,plain,
( ? [X0: $int,X1: $int,X2: $int,X3: $int] :
( $less($sum(X1,X3),$sum(X0,$uminus(X2)))
& ? [X4: $int] :
( p(X4,X2,X3)
& p(X4,X0,X1) ) )
=> ( $less($sum(sK1,sK3),$sum(sK0,$uminus(sK2)))
& ? [X4: $int] :
( p(X4,sK2,sK3)
& p(X4,sK0,sK1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f22,plain,
( ? [X4: $int] :
( p(X4,sK2,sK3)
& p(X4,sK0,sK1) )
=> ( p(sK4,sK2,sK3)
& p(sK4,sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
tff(f23,plain,
( $less($sum(sK1,sK3),$sum(sK0,$uminus(sK2)))
& p(sK4,sK2,sK3)
& p(sK4,sK0,sK1)
& ! [X5: $int,X6: $int,X7: $int] :
( ( ( ~ $less($sum(X6,X7),X5)
& ~ $less(X5,$sum(X6,$uminus(X7))) )
| ~ p(X5,X6,X7) )
& ( p(X5,X6,X7)
| $less($sum(X6,X7),X5)
| $less(X5,$sum(X6,$uminus(X7))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f20,f22,f21]) ).
tff(f25,plain,
! [X6: $int,X7: $int,X5: $int] :
( ~ $less(X5,$sum(X6,$uminus(X7)))
| ~ p(X5,X6,X7) ),
inference(cnf_transformation,[],[f23]) ).
tff(f26,plain,
! [X6: $int,X7: $int,X5: $int] :
( ~ $less($sum(X6,X7),X5)
| ~ p(X5,X6,X7) ),
inference(cnf_transformation,[],[f23]) ).
tff(f27,plain,
p(sK4,sK0,sK1),
inference(cnf_transformation,[],[f23]) ).
tff(f28,plain,
p(sK4,sK2,sK3),
inference(cnf_transformation,[],[f23]) ).
tff(f29,plain,
$less($sum(sK1,sK3),$sum(sK0,$uminus(sK2))),
inference(cnf_transformation,[],[f23]) ).
cnf(c_61,negated_conjecture,
$less_int($sum_int(sK1,sK3),$sum_int(sK0,$uminus_int(sK2))),
inference(cnf_transformation,[],[f29]) ).
cnf(c_62,negated_conjecture,
p(sK4,sK2,sK3),
inference(cnf_transformation,[],[f28]) ).
cnf(c_63,negated_conjecture,
p(sK4,sK0,sK1),
inference(cnf_transformation,[],[f27]) ).
cnf(c_64,negated_conjecture,
( ~ $less_int($sum_int(X0_3,X1_3),X2_3)
| ~ p(X2_3,X0_3,X1_3) ),
inference(cnf_transformation,[],[f26]) ).
cnf(c_65,negated_conjecture,
( ~ $less_int(X0_3,$sum_int(X1_3,$uminus_int(X2_3)))
| ~ p(X0_3,X1_3,X2_3) ),
inference(cnf_transformation,[],[f25]) ).
cnf(c_86,plain,
( ~ $less_int($sum_int(X0_3,X1_3),X2_3)
| ~ p(X2_3,X0_3,X1_3) ),
inference(prop_impl_just,[status(thm)],[c_64]) ).
cnf(c_90,plain,
( ~ $less_int(X0_3,$sum_int(X1_3,$uminus_int(X2_3)))
| ~ p(X0_3,X1_3,X2_3) ),
inference(prop_impl_just,[status(thm)],[c_65]) ).
cnf(c_228,plain,
( X0_3 != sK2
| X1_3 != sK3
| X2_3 != sK4
| ~ $less_int($sum_int(X0_3,X1_3),X2_3) ),
inference(resolution_lifted,[status(thm)],[c_62,c_86]) ).
cnf(c_229,plain,
~ $less_int($sum_int(sK2,sK3),sK4),
inference(unflattening,[status(thm)],[c_228]) ).
cnf(c_243,plain,
( X0_3 != sK0
| X1_3 != sK1
| X2_3 != sK4
| ~ $less_int(X2_3,$sum_int(X0_3,$uminus_int(X1_3))) ),
inference(resolution_lifted,[status(thm)],[c_63,c_90]) ).
cnf(c_244,plain,
~ $less_int(sK4,$sum_int(sK0,$uminus_int(sK1))),
inference(unflattening,[status(thm)],[c_243]) ).
cnf(c_4959,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_244,c_229,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ARI616_1 : TPTP v8.1.2. Released v5.1.0.
% 0.06/0.12 % Command : run_iprover %s %d THM
% 0.11/0.32 % Computer : n022.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri May 3 00:58:12 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.17/0.43 Running TFA theorem proving
% 0.17/0.43 Running: /export/starexec/sandbox2/solver/bin/run_problem --no_cores 8 --schedule casc_29_tfa --heuristic_context casc_unsat /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.20/1.12 % SZS status Started for theBenchmark.p
% 3.20/1.12 % SZS status Theorem for theBenchmark.p
% 3.20/1.12
% 3.20/1.12 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.20/1.12
% 3.20/1.12 ------ iProver source info
% 3.20/1.12
% 3.20/1.12 git: date: 2024-05-02 19:28:25 +0000
% 3.20/1.12 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.20/1.12 git: non_committed_changes: false
% 3.20/1.12
% 3.20/1.12 ------ Parsing...
% 3.20/1.12 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.20/1.12
% 3.20/1.12 ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 3.20/1.12
% 3.20/1.12 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.20/1.12
% 3.20/1.12 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.20/1.12 ------ Proving...
% 3.20/1.12 ------ Problem Properties
% 3.20/1.12
% 3.20/1.12
% 3.20/1.12 clauses 17
% 3.20/1.12 conjectures 1
% 3.20/1.12 EPR 4
% 3.20/1.12 Horn 15
% 3.20/1.12 unary 13
% 3.20/1.12 binary 2
% 3.20/1.12 lits 23
% 3.20/1.12 lits eq 7
% 3.20/1.12 fd_pure 0
% 3.20/1.12 fd_pseudo 0
% 3.20/1.12 fd_cond 0
% 3.20/1.12 fd_pseudo_cond 1
% 3.20/1.12 AC symbols 1
% 3.20/1.12
% 3.20/1.12 ------ Input Options Time Limit: Unbounded
% 3.20/1.12
% 3.20/1.12
% 3.20/1.12 ------
% 3.20/1.12 Current options:
% 3.20/1.12 ------
% 3.20/1.12
% 3.20/1.12
% 3.20/1.12
% 3.20/1.12
% 3.20/1.12 ------ Proving...
% 3.20/1.12
% 3.20/1.12
% 3.20/1.12 % SZS status Theorem for theBenchmark.p
% 3.20/1.12
% 3.20/1.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.20/1.12
% 3.20/1.12
%------------------------------------------------------------------------------