TSTP Solution File: SWW538_5 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SWW538_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n021.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 : Mon Jun 24 18:33:26 EDT 2024
% Result : Theorem 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 15 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-4 aty)
% Number of functors : 34 ( 34 usr; 5 con; 0-5 aty)
% Number of variables : 29 ( 27 !; 2 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
a: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
huffma1450048681e_tree: $tType > $tType ).
tff(type_def_8,type,
int: $tType ).
tff(type_def_9,type,
nat: $tType ).
tff(type_def_10,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_1,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_2,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_3,type,
huffma675207370phabet:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > fun(X0,bool) ) ).
tff(func_def_4,type,
huffma854194513Weight:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_5,type,
huffma1134658180e_cost:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_6,type,
huffma410068972_depth:
!>[X0: $tType] : ( ( huffma1450048681e_tree(X0) * X0 ) > nat ) ).
tff(func_def_7,type,
huffma1352802255e_freq:
!>[X0: $tType] : ( ( huffma1450048681e_tree(X0) * X0 ) > nat ) ).
tff(func_def_8,type,
huffma945805758height:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_9,type,
huffma1146269203erNode:
!>[X0: $tType] : ( ( nat * huffma1450048681e_tree(X0) * huffma1450048681e_tree(X0) ) > huffma1450048681e_tree(X0) ) ).
tff(func_def_10,type,
huffma2021818691e_Leaf:
!>[X0: $tType] : ( ( nat * X0 ) > huffma1450048681e_tree(X0) ) ).
tff(func_def_11,type,
huffma107959123e_case:
!>[X0: $tType,X1: $tType] : ( ( fun(nat,fun(X0,X1)) * fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))) * huffma1450048681e_tree(X0) ) > X1 ) ).
tff(func_def_12,type,
huffma1280178957ee_rec:
!>[X0: $tType,X1: $tType] : ( ( fun(nat,fun(X0,X1)) * fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))) * huffma1450048681e_tree(X0) ) > X1 ) ).
tff(func_def_13,type,
huffma1926487300e_size:
!>[X0: $tType] : ( ( fun(X0,nat) * huffma1450048681e_tree(X0) ) > nat ) ).
tff(func_def_14,type,
huffma921447403eTrees:
!>[X0: $tType] : ( ( huffma1450048681e_tree(X0) * huffma1450048681e_tree(X0) ) > huffma1450048681e_tree(X0) ) ).
tff(func_def_15,type,
huffma83463279weight:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_16,type,
if:
!>[X0: $tType] : ( ( bool * X0 * X0 ) > X0 ) ).
tff(func_def_17,type,
suc: nat > nat ).
tff(func_def_18,type,
nat_size: nat > nat ).
tff(func_def_19,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
tff(func_def_20,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_21,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_22,type,
fFalse: bool ).
tff(func_def_23,type,
fTrue: bool ).
tff(func_def_24,type,
t_1: huffma1450048681e_tree(a) ).
tff(func_def_25,type,
t_2: huffma1450048681e_tree(a) ).
tff(func_def_26,type,
sK0: a ).
tff(func_def_27,type,
sK1:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_28,type,
sK2:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > huffma1450048681e_tree(X0) ) ).
tff(func_def_29,type,
sK3:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > huffma1450048681e_tree(X0) ) ).
tff(func_def_30,type,
sK4:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_31,type,
sK5:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).
tff(pred_def_1,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
semiring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
comm_monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
huffma1518433673istent:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > $o ) ).
tff(pred_def_14,type,
nat_tr1645093318rphism:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * fun(X0,bool) ) > $o ) ).
tff(pred_def_15,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_16,type,
pp: bool > $o ).
tff(pred_def_17,type,
sP6: nat > $o ).
tff(f314,plain,
$false,
inference(resolution,[],[f293,f200]) ).
tff(f200,plain,
~ sP6(plus_plus(nat,huffma1352802255e_freq(a,t_1,sK0),huffma1352802255e_freq(a,t_2,sK0))),
introduced(inequality_splitting_name_introduction,[new_symbols(naming,[sP6])]) ).
tff(f293,plain,
sP6(plus_plus(nat,huffma1352802255e_freq(a,t_1,sK0),huffma1352802255e_freq(a,t_2,sK0))),
inference(backward_demodulation,[],[f201,f176]) ).
tff(f176,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0),X4: X0] : ( huffma1352802255e_freq(X0,huffma1146269203erNode(X0,X3,X2,X1),X4) = plus_plus(nat,huffma1352802255e_freq(X0,X2,X4),huffma1352802255e_freq(X0,X1,X4)) ),
inference(cnf_transformation,[],[f134]) ).
tff(f134,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat,X4: X0] : ( huffma1352802255e_freq(X0,huffma1146269203erNode(X0,X3,X2,X1),X4) = plus_plus(nat,huffma1352802255e_freq(X0,X2,X4),huffma1352802255e_freq(X0,X1,X4)) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X0: $tType,X9: huffma1450048681e_tree(X0),X10: huffma1450048681e_tree(X0),X11: nat,X12: X0] : ( huffma1352802255e_freq(X0,huffma1146269203erNode(X0,X11,X10,X9),X12) = plus_plus(nat,huffma1352802255e_freq(X0,X10,X12),huffma1352802255e_freq(X0,X9,X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
tff(f201,plain,
sP6(huffma1352802255e_freq(a,huffma1146269203erNode(a,plus_plus(nat,huffma854194513Weight(a,t_1),huffma854194513Weight(a,t_2)),t_1,t_2),sK0)),
inference(inequality_splitting,[],[f199,f200]) ).
tff(f199,plain,
plus_plus(nat,huffma1352802255e_freq(a,t_1,sK0),huffma1352802255e_freq(a,t_2,sK0)) != huffma1352802255e_freq(a,huffma1146269203erNode(a,plus_plus(nat,huffma854194513Weight(a,t_1),huffma854194513Weight(a,t_2)),t_1,t_2),sK0),
inference(definition_unfolding,[],[f168,f179]) ).
tff(f179,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X1: huffma1450048681e_tree(X0)] : ( huffma921447403eTrees(X0,X2,X1) = huffma1146269203erNode(X0,plus_plus(nat,huffma854194513Weight(X0,X2),huffma854194513Weight(X0,X1)),X2,X1) ),
inference(cnf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0)] : ( huffma921447403eTrees(X0,X2,X1) = huffma1146269203erNode(X0,plus_plus(nat,huffma854194513Weight(X0,X2),huffma854194513Weight(X0,X1)),X2,X1) ),
inference(rectify,[],[f20]) ).
tff(f20,axiom,
! [X0: $tType,X9: huffma1450048681e_tree(X0),X10: huffma1450048681e_tree(X0)] : ( huffma921447403eTrees(X0,X10,X9) = huffma1146269203erNode(X0,plus_plus(nat,huffma854194513Weight(X0,X10),huffma854194513Weight(X0,X9)),X10,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
tff(f168,plain,
huffma1352802255e_freq(a,huffma921447403eTrees(a,t_1,t_2),sK0) != plus_plus(nat,huffma1352802255e_freq(a,t_1,sK0),huffma1352802255e_freq(a,t_2,sK0)),
inference(cnf_transformation,[],[f155]) ).
tff(f155,plain,
huffma1352802255e_freq(a,huffma921447403eTrees(a,t_1,t_2),sK0) != plus_plus(nat,huffma1352802255e_freq(a,t_1,sK0),huffma1352802255e_freq(a,t_2,sK0)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f149,f154]) ).
tff(f154,plain,
( ? [X0: a] : ( huffma1352802255e_freq(a,huffma921447403eTrees(a,t_1,t_2),X0) != plus_plus(nat,huffma1352802255e_freq(a,t_1,X0),huffma1352802255e_freq(a,t_2,X0)) )
=> ( huffma1352802255e_freq(a,huffma921447403eTrees(a,t_1,t_2),sK0) != plus_plus(nat,huffma1352802255e_freq(a,t_1,sK0),huffma1352802255e_freq(a,t_2,sK0)) ) ),
introduced(choice_axiom,[]) ).
tff(f149,plain,
? [X0: a] : ( huffma1352802255e_freq(a,huffma921447403eTrees(a,t_1,t_2),X0) != plus_plus(nat,huffma1352802255e_freq(a,t_1,X0),huffma1352802255e_freq(a,t_2,X0)) ),
inference(ennf_transformation,[],[f128]) ).
tff(f128,plain,
~ ! [X0: a] : ( huffma1352802255e_freq(a,huffma921447403eTrees(a,t_1,t_2),X0) = plus_plus(nat,huffma1352802255e_freq(a,t_1,X0),huffma1352802255e_freq(a,t_2,X0)) ),
inference(rectify,[],[f127]) ).
tff(f127,negated_conjecture,
~ ! [X48: a] : ( huffma1352802255e_freq(a,huffma921447403eTrees(a,t_1,t_2),X48) = plus_plus(nat,huffma1352802255e_freq(a,t_1,X48),huffma1352802255e_freq(a,t_2,X48)) ),
inference(negated_conjecture,[],[f126]) ).
tff(f126,conjecture,
! [X48: a] : ( huffma1352802255e_freq(a,huffma921447403eTrees(a,t_1,t_2),X48) = plus_plus(nat,huffma1352802255e_freq(a,t_1,X48),huffma1352802255e_freq(a,t_2,X48)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW538_5 : TPTP v8.2.0. Released v6.0.0.
% 0.07/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n021.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 : Wed Jun 19 07:41:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 This is a TF1_THM_EQU_NAR problem
% 0.12/0.36 Running first-order theorem proving
% 0.12/0.36 Running /export/starexec/sandbox/solver/bin/vampire --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.41 % (13550)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.41 % (13557)dis+1010_159245:1048576_to=lpo:sil=2000:etr=on:sp=unary_frequency:spb=goal:rnwc=on:nwc=10.9066:st=2:i=124:sd=1:nm=3:av=off:ss=axioms:rawr=on:drc=encompass:foolp=on:sgt=5:cond=fast:er=filter:erape=on:erml=2:s2a=on_0 on theBenchmark for (2999ds/124Mi)
% 0.20/0.42 % (13550)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (13556)dis+1010_1:1_sil=2000:nwc=3.0:s2a=on:i=132:ins=5:fsr=off:ss=axioms:sd=2:fd=off_0 on theBenchmark for (2999ds/132Mi)
% 0.20/0.42 % (13550)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (13554)lrs+10_1:3_drc=off:sil=256000:sp=unary_first:lwlo=on:i=216875:kws=precedence:ins=3:rawr=on:nwc=10.0_0 on theBenchmark for (2999ds/216875Mi)
% 0.20/0.42 % (13550)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (13555)dis+1011_3:1_sil=256000:tgt=ground:sac=on:i=109:sd=1:ss=included_0 on theBenchmark for (2999ds/109Mi)
% 0.20/0.42 % (13550)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (13553)lrs+1010_2201:262144_anc=all:drc=encompass:sil=256000:sims=off:sp=frequency:spb=goal_then_units:rp=on:lwlo=on:st=3.0:i=179501:bs=unit_only:nm=6:ins=2:fsd=on:ss=axioms:sgt=16:afr=on:tgt=ground:awrs=decay:awrsf=200:acc=on:ccuc=first_0 on theBenchmark for (2999ds/179501Mi)
% 0.20/0.42 % (13550)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (13552)dis+11_1:1_nwc=5.0:s2a=on:i=66616:s2at=3.0:sil=128000:bd=off_0 on theBenchmark for (2999ds/66616Mi)
% 0.20/0.43 % (13550)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43 % (13551)lrs+1011_1:12_anc=none:drc=off:sil=64000:sims=off:sp=unary_first:spb=goal_then_units:lsd=20:rnwc=on:nwc=2.0:i=53554:add=off:awrs=converge:bd=off:uhcvi=on:tgt=ground:afp=300:afq=1.63_0 on theBenchmark for (2999ds/53554Mi)
% 0.20/0.43 % (13556)First to succeed.
% 0.20/0.43 % (13557)Also succeeded, but the first one will report.
% 0.20/0.43 % (13556)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-13550"
% 0.20/0.43 % (13550)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.43 % (13556)Refutation found. Thanks to Tanya!
% 0.20/0.43 % SZS status Theorem for theBenchmark
% 0.20/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.43 % (13556)------------------------------
% 0.20/0.43 % (13556)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.20/0.43 % (13556)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.20/0.43 % (13556)Termination reason: Refutation
% 0.20/0.43
% 0.20/0.43 % (13556)Memory used [KB]: 1223
% 0.20/0.43 % (13556)Time elapsed: 0.008 s
% 0.20/0.43 % (13556)Instructions burned: 10 (million)
% 0.20/0.43 % (13556)------------------------------
% 0.20/0.43 % (13556)------------------------------
% 0.20/0.43 % (13550)Success in time 0.053 s
%------------------------------------------------------------------------------