%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n014.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 01:40:24 PM UTC 2026
% Result : Theorem 0.31s 0.38s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 10 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 18 ( 16 usr; 1 prp; 0-4 aty)
% Number of functors : 40 ( 40 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:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_27,type,
sK1:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).
tff(func_def_28,type,
sK2:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
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) > huffma1450048681e_tree(X0) ) ).
tff(func_def_31,type,
sK5:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).
tff(func_def_32,type,
sK6:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_33,type,
sK7: nat > nat ).
tff(func_def_34,type,
sK8: fun(nat,bool) > nat ).
tff(func_def_35,type,
sK9: nat > nat ).
tff(func_def_36,type,
sK10: fun(nat,bool) > nat ).
tff(func_def_37,type,
sK11: 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(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(f176,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(f185,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(f203,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(f334,plain,
huffma1352802255e_freq(a,huffma921447403eTrees(a,t_1,t_2),sK11) != plus_plus(nat,huffma1352802255e_freq(a,t_1,sK11),huffma1352802255e_freq(a,t_2,sK11)),
inference(cnf_transformation,[],[f176]) ).
tff(f335,plain,
plus_plus(nat,huffma1352802255e_freq(a,t_1,sK11),huffma1352802255e_freq(a,t_2,sK11)) != huffma1352802255e_freq(a,huffma1146269203erNode(a,plus_plus(nat,huffma854194513Weight(a,t_1),huffma854194513Weight(a,t_2)),t_1,t_2),sK11),
inference(definition_unfolding,[],[f334,f203]) ).
tff(f956,plain,
$false,
inference(backward_subsumption_resolution,[],[f335,f185]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.09/0.22 % Computer : n014.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Mon Sep 28 14:17:30 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.28 Running first-order model finding
% 0.09/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.31/0.38 % (1799537)Will run a generic schedule for satisfiability detection.
% 0.31/0.38 % (1799542)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=125586527_2999 on theBenchmark for (2999ds/0Mi)
% 0.31/0.38 % Exception at run slice level
% 0.31/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.31/0.38 % (1799543)% WARNING: option uhcvi not known.
% 0.31/0.38 % (1799545)dis+10_1_sil=32000:sp=arity:random_seed=3040807195:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.31/0.38 % (1799546)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3200156227:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.31/0.38 % (1799547)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1347174244:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.31/0.38 % (1799543)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2868421118:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.31/0.38 % (1799544)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=121243841:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.31/0.38 % (1799548)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=373673213:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.31/0.38 % (1799550)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2075820138:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.31/0.38 % Exception at run slice level
% 0.31/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.31/0.38 % (1799558)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=945845200:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.31/0.38 % (1799543) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1799537-1799543"...
% 0.31/0.38 % (1799543)...printing done.
% 0.31/0.38 % (1799543)Refutation found. Thanks to Tanya!
% 0.31/0.38 % SZS status Theorem for theBenchmark
% 0.31/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.31/0.38 % (1799543)------------------------------
% 0.31/0.38 % (1799543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.38 % (1799543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.38 % (1799543)CaDiCaL version: 2.1.3
% 0.31/0.38 % (1799543)Termination reason: Refutation
% 0.31/0.38 % (1799543)Time elapsed: 0.043 s
% 0.31/0.38 % (1799543)Peak memory usage: 12 MB
% 0.31/0.38 % (1799543)Instructions burned: 41 (million)
% 0.31/0.38 % (1799537)Success in time 0.085 s
% 0.31/0.38 % Vampire exiting
%------------------------------------------------------------------------------