%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW538_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 : Tue Sep 29 01:30:46 PM UTC 2026
% Result : Theorem 0.27s 2.06s
% Output : Refutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 14 unt; 0 typ; 1 def)
% Number of atoms : 14 ( 10 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 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 : 29 ( 29 usr; 5 con; 0-5 aty)
% Number of variables : 19 ( 18 !; 1 ?; 19 :)
% 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(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,
sP1: nat > $o ).
tff(f5,axiom,
! [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)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_freq_Osimps_I2_J) ).
tff(f20,axiom,
! [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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_uniteTrees__def) ).
tff(f126,conjecture,
! [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)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f127,negated_conjecture,
~ ! [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(negated_conjecture,[status(cth)],[f126]) ).
tff(f129,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,[],[f127]) ).
tff(f131,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(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f129]) ).
tff(f134,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,[],[f131]) ).
tff(f144,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,[],[f5]) ).
tff(f145,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,[],[f20]) ).
tff(f146,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,[],[f134,f145]) ).
tff(f147,definition,
~ sP1(plus_plus(nat,huffma1352802255e_freq(a,t_1,sK0),huffma1352802255e_freq(a,t_2,sK0))),
introduced(definition,[new_symbols(definition,[sP1])],[inequality_splitting_name_introduction]) ).
tff(f148,plain,
sP1(huffma1352802255e_freq(a,huffma1146269203erNode(a,plus_plus(nat,huffma854194513Weight(a,t_1),huffma854194513Weight(a,t_2)),t_1,t_2),sK0)),
inference(inequality_splitting,[],[f146,f147]) ).
tff(f152,plain,
sP1(plus_plus(nat,huffma1352802255e_freq(a,t_1,sK0),huffma1352802255e_freq(a,t_2,sK0))),
inference(forward_demodulation,[],[f148,f144]) ).
tff(f153,plain,
$false,
inference(forward_subsumption_resolution,[],[f152,f147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW538_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 % Computer : n015.cluster.edu
% 0.09/0.24 % Model : x86_64 x86_64
% 0.09/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.24 % Memory : 8046.5625MB
% 0.09/0.24 % OS : Linux 6.8.0-71-generic
% 0.09/0.24 % CPULimit : 300
% 0.09/0.24 % WCLimit : 300
% 0.09/0.24 % DateTime : Mon Sep 28 14:21:02 UTC 2026
% 0.09/0.24 % CPUTime :
% 0.09/0.24 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.30 Running first-order theorem proving
% 0.23/0.30 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.27/2.06 % (2655264)Detected formulas, will run a generic FOF schedule.
% 0.27/2.06 % (2655278)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=4162305755:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.27/2.06 % (2655280)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1507849370:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.27/2.06 % (2655284)dis-21_1_sil=8000:lcm=predicate:random_seed=3451822442:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.27/2.06 % (2655279)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3489122137:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.27/2.06 % (2655281)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1746956293:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.27/2.06 % (2655282)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=264088646:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.27/2.06 % (2655283)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1694252834:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.27/2.06 % (2655281)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.27/2.06 % (2655281)First to succeed.
% 0.27/2.06 % (2655281)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2655264"
% 0.27/2.06 % (2655280)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.27/2.06 % (2655282)Also succeeded, but the first one will report.
% 0.27/2.06 % (2655284)Also succeeded, but the first one will report.
% 0.27/2.06 % (2655283)Also succeeded, but the first one will report.
% 0.27/2.06 % Exception at run slice level
% 0.27/2.06 User error: GNN currently only supports monomorphic FOL.
% 0.27/2.06 % (2655281)Refutation found. Thanks to Tanya!
% 0.27/2.06 % SZS status Theorem for theBenchmark
% 0.27/2.06 % SZS output start Proof for theBenchmark
% See solution above
% 0.27/2.06 % (2655281)------------------------------
% 0.27/2.06 % (2655281)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.27/2.06 % (2655281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/2.06 % (2655281)CaDiCaL version: 2.1.3
% 0.27/2.06 % (2655281)Termination reason: Refutation
% 0.27/2.06 % (2655281)Time elapsed: 0.005 s
% 0.27/2.06 % (2655281)Peak memory usage: 88 MB
% 0.27/2.06 % (2655281)Instructions burned: 2 (million)
% 0.27/2.06 % (2655281)------------------------------
% 0.27/2.06 % (2655281)------------------------------
% 0.27/2.06 % (2655264)Success in time 0.726 s
% 0.27/2.06 % Vampire exiting
%------------------------------------------------------------------------------