%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW535_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 : n001.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 3.79s 1.32s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 16 unt; 0 typ; 1 def)
% Number of atoms : 16 ( 8 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 6 con; 0-5 aty)
% Number of variables : 14 ( 14 !; 0 ?; 14 :)
% 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,
nat: $tType ).
tff(type_def_9,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_2,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_3,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_4,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_6,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_7,type,
huffma675207370phabet:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > fun(X0,bool) ) ).
tff(func_def_8,type,
huffma1134658180e_cost:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_9,type,
huffma410068972_depth:
!>[X0: $tType] : ( ( huffma1450048681e_tree(X0) * X0 ) > nat ) ).
tff(func_def_10,type,
huffma1352802255e_freq:
!>[X0: $tType] : ( ( huffma1450048681e_tree(X0) * X0 ) > nat ) ).
tff(func_def_11,type,
huffma1146269203erNode:
!>[X0: $tType] : ( ( nat * huffma1450048681e_tree(X0) * huffma1450048681e_tree(X0) ) > huffma1450048681e_tree(X0) ) ).
tff(func_def_12,type,
huffma2021818691e_Leaf:
!>[X0: $tType] : ( ( nat * X0 ) > huffma1450048681e_tree(X0) ) ).
tff(func_def_13,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_14,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_15,type,
huffma83463279weight:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_16,type,
inf_inf:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_17,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
tff(func_def_18,type,
bot_bot:
!>[X0: $tType] : X0 ).
tff(func_def_19,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_20,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_21,type,
fFalse: bool ).
tff(func_def_22,type,
fTrue: bool ).
tff(func_def_23,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_24,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).
tff(func_def_25,type,
t_1: huffma1450048681e_tree(a) ).
tff(func_def_26,type,
t_2: huffma1450048681e_tree(a) ).
tff(func_def_27,type,
w: nat ).
tff(pred_def_1,type,
bounded_lattice:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
one:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
bot:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
lattice:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
semiring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
comm_monoid_add:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
ab_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
semilattice_inf:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
bounded_lattice_bot:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
cancel146912293up_add:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
semiri456707255roduct:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
huffma1518433673istent:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > $o ) ).
tff(pred_def_18,type,
pp: bool > $o ).
tff(pred_def_19,type,
sP0: nat > $o ).
tff(f4,axiom,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat] : ( huffma1134658180e_cost(X0,huffma1146269203erNode(X0,X3,X2,X1)) = plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(X0,X2),huffma1134658180e_cost(X0,X2)),huffma83463279weight(X0,X1)),huffma1134658180e_cost(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_cost_Osimps_I2_J) ).
tff(f14,axiom,
! [X0: nat,X1: nat,X2: nat] : ( plus_plus(nat,plus_plus(nat,X2,X1),X0) = plus_plus(nat,X2,plus_plus(nat,X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_nat__add__assoc) ).
tff(f133,conjecture,
huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) = plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_1),huffma1134658180e_cost(a,t_1)),huffma83463279weight(a,t_2)),huffma1134658180e_cost(a,t_2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f134,negated_conjecture,
( ( ~ huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) ) = plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_1),huffma1134658180e_cost(a,t_1)),huffma83463279weight(a,t_2)),huffma1134658180e_cost(a,t_2)) ),
inference(negated_conjecture,[status(cth)],[f133]) ).
tff(f135,plain,
huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_1),huffma1134658180e_cost(a,t_1)),huffma83463279weight(a,t_2)),huffma1134658180e_cost(a,t_2)),
inference(flattening,[],[f134]) ).
tff(f143,plain,
huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2)) != plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_1),huffma1134658180e_cost(a,t_1)),huffma83463279weight(a,t_2)),huffma1134658180e_cost(a,t_2)),
inference(cnf_transformation,[],[f135]) ).
tff(f144,plain,
! [X2: nat,X0: nat,X1: nat] : ( plus_plus(nat,X2,plus_plus(nat,X1,X0)) = plus_plus(nat,plus_plus(nat,X2,X1),X0) ),
inference(cnf_transformation,[],[f14]) ).
tff(f152,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] : ( huffma1134658180e_cost(X0,huffma1146269203erNode(X0,X3,X2,X1)) = plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(X0,X2),huffma1134658180e_cost(X0,X2)),huffma83463279weight(X0,X1)),huffma1134658180e_cost(X0,X1)) ),
inference(cnf_transformation,[],[f4]) ).
tff(f159,definition,
~ sP0(huffma1134658180e_cost(a,huffma1146269203erNode(a,w,t_1,t_2))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
tff(f160,plain,
sP0(plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_1),huffma1134658180e_cost(a,t_1)),huffma83463279weight(a,t_2)),huffma1134658180e_cost(a,t_2))),
inference(inequality_splitting,[],[f143,f159]) ).
tff(f166,plain,
~ sP0(plus_plus(nat,plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_1),huffma1134658180e_cost(a,t_1)),huffma83463279weight(a,t_2)),huffma1134658180e_cost(a,t_2))),
inference(forward_demodulation,[],[f159,f152]) ).
tff(f167,plain,
sP0(plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_1),huffma1134658180e_cost(a,t_1)),plus_plus(nat,huffma83463279weight(a,t_2),huffma1134658180e_cost(a,t_2)))),
inference(forward_demodulation,[],[f160,f144]) ).
tff(f168,plain,
~ sP0(plus_plus(nat,plus_plus(nat,huffma83463279weight(a,t_1),huffma1134658180e_cost(a,t_1)),plus_plus(nat,huffma83463279weight(a,t_2),huffma1134658180e_cost(a,t_2)))),
inference(forward_demodulation,[],[f166,f144]) ).
tff(f169,plain,
sP0(plus_plus(nat,huffma83463279weight(a,t_1),plus_plus(nat,huffma1134658180e_cost(a,t_1),plus_plus(nat,huffma83463279weight(a,t_2),huffma1134658180e_cost(a,t_2))))),
inference(forward_demodulation,[],[f167,f144]) ).
tff(f170,plain,
~ sP0(plus_plus(nat,huffma83463279weight(a,t_1),plus_plus(nat,huffma1134658180e_cost(a,t_1),plus_plus(nat,huffma83463279weight(a,t_2),huffma1134658180e_cost(a,t_2))))),
inference(forward_demodulation,[],[f168,f144]) ).
tff(f171,plain,
$false,
inference(forward_subsumption_resolution,[],[f170,f169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW535_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n001.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 14:23:48 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 3.79/1.32 % (373835)Detected formulas, will run a generic FOF schedule.
% 3.79/1.32 % (373842)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=806068643:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.79/1.32 % (373842)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.79/1.32 % (373846)dis-21_1_sil=8000:lcm=predicate:random_seed=774822331: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)
% 3.79/1.32 % (373845)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2374484264:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.79/1.32 % (373841)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=1707758377:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.79/1.32 % (373843)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=9056317:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.79/1.32 % (373844)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1166512428:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.79/1.32 % (373840)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=955604909:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.79/1.32 % (373843)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.79/1.32 % (373843)First to succeed.
% 3.79/1.32 % (373843)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-373835"
% 3.79/1.32 % (373846)Also succeeded, but the first one will report.
% 3.79/1.32 % (373844)Also succeeded, but the first one will report.
% 3.79/1.32 % (373845)Also succeeded, but the first one will report.
% 3.79/1.32 % Exception at run slice level
% 3.79/1.32 User error: GNN currently only supports monomorphic FOL.
% 3.79/1.32 % (373843)Refutation found. Thanks to Tanya!
% 3.79/1.32 % SZS status Theorem for theBenchmark
% 3.79/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.79/1.32 % (373843)------------------------------
% 3.79/1.32 % (373843)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.32 % (373843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.32 % (373843)CaDiCaL version: 2.1.3
% 3.79/1.32 % (373843)Termination reason: Refutation
% 3.79/1.32 % (373843)Time elapsed: 0.003 s
% 3.79/1.32 % (373843)Peak memory usage: 89 MB
% 3.79/1.32 % (373843)Instructions burned: 2 (million)
% 3.79/1.32 % (373843)------------------------------
% 3.79/1.32 % (373843)------------------------------
% 3.79/1.32 % (373835)Success in time 0.446 s
% 3.79/1.32 % Vampire exiting
%------------------------------------------------------------------------------